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<image>A soap film ( $n=4 / 3$ ) of thickness $d$ is illuminated at normal incidence by light of wavelength 500 nm . Calculate the approximate intensities of interference maxima relative to the incident intensity as $d$ is varied, when viewed in reflected light.
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1
<image>As shown in Fig. 3.26, the switch has been in position A for a long time. At $t=0$ it is suddenly moved to position B. Immediately after contact with B: What is the time rate of change of the current through $R$ ?
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<image>At low temperatures, a mixture of ${ }^{3} \text{He}$ and ${ }^{4} \text{He}$ atoms form a liquid which separates into two phases: a concentrated phase (nearly pure ${ }^{3} \text{He}$), and a dilute phase (roughly $6.5 \text{\textperthousand} { }^{3} \text{He}$ for $T \text{\textless}= 0.1 \text{ K}$). The ligh...
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<image>The current-voltage characteristic of the output terminals A, B (Fig. 3.3) is the same as that of a battery of emf $\varepsilon_{0}$ and internal resistance $r$. Find the short-circuit current provided by the battery.
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<image>A block of mass $M$ is rigidly connected to a massless circular track of radius $a$ on a frictionless horizontal table as shown in Fig. 2.7. A particle of mass $m$ is confined to move without friction on the circular track which is vertical. Set up the Lagrangian, using $\theta$ as one coordinate.
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<image>A block of mass $M$ is rigidly connected to a massless circular track of radius $a$ on a frictionless horizontal table as shown in Fig. 2.7. A particle of mass $m$ is confined to move without friction on the circular track which is vertical. In the limit of small angles, solve that equations of motion for $\thet...
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<image>A useful optical grating configuration is to diffract light back along itself. If there are $N$ grating lines per unit length, what wavelength(s) is (are) diffracted back at the incident angle $\theta$, where $\theta$ is the angle between the normal to the grating and the incident direction?
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<image>Static charges are distributed along the $x$-axis in the interval $-a \le x' \le a$. The charge density is $\rho(x')$ for $|x'| \le a$ and $0$ for $|x'| > a$. Derive a multipole expansion for the potential valid for $x>a$.
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<image>A horizontal ray of light passes through a prism of index 1.50 and apex angle $4^{\\circ}$ and then strikes a vertical mirror, as shown in the figure. Through what angle must the mirror be rotated if after reflection the ray is to be horisontal?
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<image>A simple pendulum is attached to a support which is driven horizontally with time as shown in Fig. 2.25. Set up the Lagrangian for the system in terms of the generalized coordinates $\theta$ and $y$, where $\theta$ is the angular displacement from equilibrium and $y(t)$ is the horizontal position of the pendulum...
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10
<image>As in Fig. $2.39$, what is the direction of the current in the resistor $r$ (from $A$ to $B$ or from $B$ to $A$) when the following operations are performed? In each case give a brief explanation of your reasoning? The switch $S$ is closed.
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<image>The figure below shows an apparatus for the determination of $C_{p} / C_{v}$ for a gas, according to the method of Clement and Desormes. A bottle $G$, of reasonable capacity (say a few litres), is fitted with a tap $H$, and a manometer $M$. The difference in pressure between the inside and the outside can thus b...
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<image>A beam of neutrons (mass $m$ ) traveling with nonrelativistic speed $v$ impinges on the system shown in Fig. 1.7, with beam-splitting mirrors at corners $B$ and $D$, mirrors at $A$ and $C$, and a neutron detector at $E$. The corners all make right angles, and neither the mirrors nor the beam-splitters affect the...
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<image>A long solenoid of radius $b$ and length $l$ is wound so that the axial magnetic field is $$\mathbf{B}=\begin{cases} B_{0}\,\mathbf{e}_{z}, & r<b,\\ 0, & r>b, \end{cases}$$ A particle of charge $q$ is emitted with velocity $v$ perpendicular to a central rod of radius $a$ (see Fig. 2.59). The electric force on th...
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<image>Three point particles, two of mass $m$ and one of mass $M$, are constrained to lie on a horizontal circle of radius $r$. They are mutually connected by springs, each of constant $K$, that follow the arc of the circle and that are of equal length when the system is at rest as shown in Fig. 2.48. Assuming motion t...
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<image>Four identical coherent monochromatic wave sources A, B, C, D, as shown in Fig. 4.2 produce waves of the same wavelength $\lambda$. Two receivers $R_{1}$ and $R_{2}$ are at great (but equal) distances from $B$. Which receiver, if any, picks up the greater signal if source $B$ is turned off?
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<image>Consider a solid cylinder of mass $m$ and radius $r$ sliding without rolling down the smooth inclined face of a wedge of mass $M$ that is free to move on a horizontal plane without friction (Fig. 1.174). Now suppose that the cylinder is free to roll down the wedge without slipping. How far does the wedge move in...
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<image>The one-dimensional quantum mechanical potential energy of a particle of mass $m$ is given by $$ V(x)=\begin{cases} V_{0}\delta(x), & -a<x<\infty \\ \infty, & x<-a \end{cases} $$ as shown in Fig. 1.19. At time $t=0$, the wave function of the particle is completely confined to the region $-a<x<0$. [Define the qua...
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<image>A long‐range rocket is fired from the surface of the earth (radius $R$) with velocity $\mathbf{v}=(v_r, v_\theta)$ (Fig. 1.29). Neglecting air friction and the rotation of the earth (but using the exact gravitational field), obtain an equation to determine the maximum height $H$ achieved by the trajectory.
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<image>1093 A block of mass $m$ slides without friction on an inclined plane of mass $M$ which in turn is free to slide without friction on a horizontal table (Fig. 1.65). Write sufficient equations to find the motion of the block and the inclined plane. You do not need to solve these equations. (Wisconsin)
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<image><image><image>For a particle of charge $q$, what are the energies and energy eigenfunctions if a very long solenoid containing a magnetic flux passes the doubled ring of (b) as shown in the Fig. 4.9? Assume the system does not radiate electromagnetically.
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<image>As in Fig. 4.17, two coaxial cylindrical conductors with $r_{1}$ and $r_{2}$ form a waveguide. The region between the conductors is vacuum for $z<0$ and is filled with a dielectric medium with dielectric constant $\varepsilon \neq 1$ for $z>0$. Describe the TEM mode for $z<0$ and $z>0$.
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22
<image>Figure 1.10 shows two capacitors in series, the rigid center section of length $b$ being movable vertically. The area of each plate is $A$. If the voltage difference between the outside plates is kept constant at $V_{0}$, what is the change in the energy stored in the capacitors if the center section is removed?
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<image><image><image><image>Suppose you have been supplied with a number of sheets of two types of optically active material. Sheets of type $P$ are perfect polarizers: they transmit (normally incident) light polarized parallel to some axis $\boldsymbol{n}$ and absorb light polarized perpendicular to $\boldsymbol{n}$. ...
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<image>The potential curves for the ground electronic state (A) and an excited electronic state (B) of a diatomic molecule are shown in Fig. 8.2. Each electronic state has a series of vibrational levels which are labelled by the quantum number $\nu$. Some molecules were initially at the lowest vibrational level of the ...
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<image>Assume all surfaces to be frictionless and the inertia of pulley and cord negligible (Fig. $1.6$). Find the horizontal force necessary to prevent any relative motion of $m_{1}$, $m_{2}$ and $M$.
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<image>Consider the circuit shown in Fig. 3.87. If one varies the frequency but not the amplitude of $V$, what is the maximum current that can flow? The minimum current? At what frequency will the minimum current be observed.
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<image>A $\pi$ meson with a momentum of $5 m_{\pi} c$ makes an elastic collision with a proton ($m_{p}=7 m_{\pi}$) which is initially at rest (Fig. 3.20). Find the momentum of the incident pion in the c.m. system.
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<image>A mass $M$ is constrained to slide without friction on the track $AB$ as shown in Fig. 2.24. A mass $m$ is connected to $M$ by a massless inextensible string. (Make small angle approximation.) Write a Lagrangian for this system.
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<image>An ideal gas is contained in a large jar of volume $V_{0}$. Fitted to the jar is a glass tube of cross-sectional area $A$ in which a metal ball of mass $M$ fits snugly. The equilibrium pressure in the jar is slightly higher than atmospheric pressure $p_{0}$ because of the weight of the ball. If the ball is displ...
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<image>Four identical coherent monochromatic wave sources A, B, C, D, as shown in Fig. 4.2 produce waves of the same wavelength $\lambda$. Two receivers $R_{1}$ and $R_{2}$ are at great (but equal) distances from $B$. Which receiver picks up the greater signal?
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31
<image><image>An object is placed 10 cm in front of a convering lens of focal length 10 cm . A diverging lens of focal length -15 cm is placed 5 cm behind the converging lens (Fig. 1.27). Find the character of the final image.
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<image>Find the electric quadrupole moment for two point charges of charge $e$ located at the ends of a line of length $2l$ that rotates with a constant angular velocity $\omega/2$ about an axis perpendicular to the line and through its center.
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33
<image>A mirror is moving through vacuum with relativistic speed $v$ in the $x$ direction. A beam of light with frequency $\omega_{i}$ is normally incident (from $x=+\infty$) on the mirror, as shown in Fig. 3.9. What is the frequency of the reflected light expressed in terms of $\omega_{i}$, $c$ and $v$?
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<image>Two small spheres of mass $M$ are suspended between two rigid supports with three identical springs of spring constant $K$ (each of unstretched length $\frac{a}{2}$). Assuming small oscillations about the equilibrium configuration, find the frequencies for the two normal modes corresponding to vertical oscillati...
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35
<image>$1254$ A rope is attached at one end to a wall and is wrapped around a capstan through an angle $\theta$. If someone pulls on the other end with a force $F$ as shown in Fig. 1.231(a), find the tension in the rope at a point between the wall and the capstan in terms of $F$, $\theta$ and $\mu_{s}$, the coefficient...
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36
<image>A car is traveling in the $x$-direction and maintains constant horizontal speed $v$. The car goes over a bump whose shape is described by $y_{0}=A[1-\cos (\pi x / l)]$ for $0 \leq x \leq 2 l ; y_{0}=0$ otherwise. Determine the motion of the center of mass of the car while passing over the bump. Represent the car...
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37
<image>Consider the ground state and \(n=2\) states of hydrogen atom. There are four corrections to the indicated level structure that must be considered to explain the various observed splitting of the levels. These corrections are: (a) Lamb shift, (b) fine structure, (c) hyperfine structure, (d) relativistic effects....
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38
<image>Two uniform cylinders are spinning independently about their axes, which are parallel. One has radius $R_{1}$ and mass $M_{1}$, the other $R_{2}$ and $M_{2}$. Initially they rotate in the same sense with angular speeds $\Omega_{1}$ and $\Omega_{2}$ respectively as shown in Fig. 1.128. They are then displaced unt...
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39
<image><image>Consider the Babinet Compensator shown in the figure (Fig.~2.76). The device is constructed from two pieces of uniaxial optical material with indices $n_{e}$ and $n_{o}$ for light polarized perpendicular and parallel to the optic axis, respectively. A narrow beam of light of vacuum wavelength $\lambda$ is...
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40
<image><image>Figure 2.75 shows two long parallel wires carrying equal and opposite steady currents $I$ and separated by a distance $2a$. Find an expression for the magnetic field strength at a point in the median plane (i.e. $xz$ plane in Fig. 2.75) lying a distance $z$ from the plane containing the wires.
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41
<image>A thin ring of mass $M$ and radius $r$ lies flat on a frictionless table. It is constrained by two extended identical springs with relaxed length $l_{0}$ ($l_{0} \gg r$) and spring constant $k$ as shown in Fig. 1.55. What are the normal modes of small oscillations and their frequencies?
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42
<image>An electric circuit consists of two resistors (resistances $R_{1}$ and $R_{2}$), a single condenser (capacitor $C$) and a variable voltage source $V$ joined together as shown in Fig. 3.83. When $V(t)$ is a very sharp pulse at $t=0$, we approximate $V(t)=A\delta(t)$. What is the time history of the potential drop...
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43
<image>A very long conducting pipe has a square cross section of its inside surface, with side $D$ as in Fig. 1.47. Far from either end of the pipe is suspended a point charge located at the center of the square cross section. Determine the electric potential at all points inside the pipe, perhaps in the form of an inf...
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44
<image>In Fig. 5.10 a point charge $e$ moves with constant velocity $v$ in the $z$ direction so that at time $t$ it is at the point $Q$ with coordinates $x=0$, $y=0, z=v t$. Find at the time $t$ and at the point $P$ with coordinates $x=b, y=0, z=0$ the vector potential $\mathbf{A}$.
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45
<image>In the circuit shown in Fig. 3.23, the resistance of $L$ is negligible and initially the switch is open and the current is zero. Find the quantity of heat dissipated in the resistance $R_{2}$ when the switch is closed and remains closed for a long time. (Notice the circuit diagram and the list of values for $V, ...
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46
<image>A perfectly uniform ball 20 cm in diameter and with a density of $5\,\mathrm{g}/\mathrm{cm}^{3}$ is rotating in free space at $1\,\mathrm{rev}/\mathrm{s}$. An intelligent flea of $10^{-3}\,\mathrm{g}$ resides in a small (massless) house fixed to the ball's surface at a rotational pole as shown in Fig. 1.197. The...
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47
<image>Consider a square loop of wire, of side length $l$, lying in the $xy$ plane as shown in Fig. 2.43. Suppose a particle of charge $q$ is moving with a constant velocity $v$, where $v \ll c$, in the $xz$-plane at a constant distance $z_{0}$ from the $xy$-plane. (Assume the particle is moving in the positive $x$ dir...
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48
<image>Consider an intrinsic semiconductor whose electronic density of states function $N(E)$ is depicted in Fig. Where is the Fermi level with respect to the valence and conduction bands?
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49
<image>Four identical masses are connected by four identical springs and constrained to move on a frictionless circle of radius $b$ as shown in Fig. 2.30. What are the frequencies of small oscillations?
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50
<image>The betatron accelerates particles through the emf induced by an increasing magnetic field within the particle's orbit. Let $\bar{B}_{1}$ be the average field within the particle orbit of radius $R$, and let $B_{2}$ be the field at the orbit (see Fig. 2.80). What must be the relationship between $\bar{B}_{1}$ an...
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51
<image>The conductors of a coaxial cable are connected to a battery and resistor as shown in Fig. 2.15. Starting from first principles find, in the region between $r_{1}$ and $r_{2}$, the Poynting vector.
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52
<image>Two infinite parallel wires separated by a distance $d$ carry equal currents $I$ in opposite directions, with $I$ increasing at the rate $\frac{dI}{dt}$. A square loop of wire of length $d$ on a side lies in the plane of the wires at a distance $d$ from one of the parallel wires, as illustrated in Fig. 2.30. Fin...
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53
<image>Two uniform discs in a vertical plane of masses $M_{1}$ and $M_{2}$ with radii $R_{1}$ and $R_{2}$ respectively have a thread wound about their circumferences, and are thus connected as shown in Fig. 1.158. The first disc has fixed frictionless horizontal axis of rotation through its center. Set up the equations...
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54
<image>In Fig. 3.37 the capacitor is originally charged to a potential difference $V$. The transformer is ideal: no winding resistance, no losses. At $t=0$ the switch is closed. Assume that the inductive impedances of the windings are very large compared with $R_{p}$ and $R_{s}$. Calculate: The initial secondary curren...
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55
<image>A rectangular coil of dimensions $a$ and $b$ and resistance $R$ moves with constant velocity $v$ into a magnetic field $\mathbf{B}$ as shown in Fig. 2.36. Derive an expression for the vector force on the coil in terms of the given parameters.
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56
<image>A parallel-plate capacitor is made of circular plates as shown in Fig. 2.10. The voltage across the plates (supplied by long resistanceless lead wires) has the time dependence $V=V_{0} \cos \omega t$. Assume $d \ll a \ll c / \omega$, so that fringing of the electric field and retardation may be ignored. What cur...
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57
<image>A ray of light enters a spherical drop of water of index $n$ as shown (Fig. 1.21). Find the angle $\phi$ which produces minimum deflection.
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58
<image><image>Consider a particle of mass m moving in a time-dependent potential $V(x, t)$ in one dimension. Write down the Schrödinger equations appropriate for two reference systems $(x, t)$ and $(x', t)$ moving with respect to each other with velocity $v$ (i.e. $x=x'+vt$).
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59
<image>Consider a rectangular waveguide, infinitely long in the $x$-direction, with a width ($y$-direction) 2 cm and a height ($z$-direction) 1 cm. The walls are perfect conductor, as in Fig. 4.13. For the lowest mode that can propagate, find the phase velocity and the group velocity.
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60
<image>Let us apply a shearing force on a rectangular solid block as shown in Fig. 2.77. Find the relation between the displacement $u$ and the applied force within elastic limits.
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61
<image>A plane monochromatic wave (wavelength $\lambda$ ) is incident on a set of 5 slits spaced at a distance $d$ (Fig. 2.55). You may assume that the width of the individual slits is much less than $d$. For the resulting interference pattern, which is focused on a screen, compute either analytically or approximately ...
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62
<image>Consider the ground state and \(n=2\) states of hydrogen atom. Indicate in the diagram (Fig. 1.14) the complete spectroscopic notation for all four states. There are four corrections to the indicated level structure that must be considered to explain the various observed splitting of the levels. These correction...
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63
<image>Consider the following energy level structure (Fig. 2.30): The ground states form an isotriplet as do the excited states (all states have a spin-parity of $0^{+}$). The ground state of $_{21}^{42}\text{Sc}$ can $\beta$-decay to the ground state of $_{20}^{42}\text{Ca}$ with a kinetic end-point energy of 5.4 MeV ...
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64
<image>Find the expression for the speed of the transverse elastic wave.
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65
<image>According to the Weinberg-Salam model, the Higgs boson $\phi$ couples to every elementary fermion $f$ ( $f$ may be a quark or lepton) in the form $$ \frac{e m_{f}}{m_{W}} \phi \bar{f} f, $$ where $m_{f}$ is the mass of the fermion $f, e$ is the charge of the electron, and $m_{W}$ is the mass of the $W$ boson. So...
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66
<image>Consider a two-dimensional classical system with Hamiltonian\n\nH=\frac{1}{2 m}\left(P_{1}^{2}+P_{2}^{2}\right)+\frac{1}{2} \mu^{2}\left(x_{1}^{2}+x_{2}^{2}\right)-\frac{1}{4} \lambda\left(x_{1}^{2}+x_{2}^{2}\right)^{2} .\n\nA system of $N$ particles of mass $m$ each is in thermal equilibrium at temperature $T$ ...
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67
<image>One mole of the paramagnetic substance whose $T S$ diagram is shown below is to be used as the working substance in a Carnot refrigerator operating between a sample at 0.2 K and a reservoir at 1 K: How much work will be performed on the paramagnetic substance per cycle?
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68
<image>A simple molecular beam apparatus is shown in Fig. 2.40. The oven contains $\mathrm{H}_{2}$ molecules at 300 K and at a pressure of 1 mm of mercury. The hole on the oven has a diameter of $100 \mu \mathrm{~m}$ which is much smaller than the molecular mean free path. After the collimating slits, the beam has a di...
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69
<image>In Fig. 2.71, the cylindrical cavity is symmetric about its long axis. For the purposes of this problem, it can be approximated as a coaxial cable (which has inductance and capacitance) shorted at one end and connected to a parallel plate disk capacitor at the other. Find the direction and radial-dependence of t...
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70
<image>Refer to Fig. 3.67. When this monostable circuit is triggered how long will $Q_{2}$ be off?
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71
<image>A dipole of fixed length $2 R$ has mass $m$ on each end, charge $+Q_{2}$ on one end and $-Q_{2}$ on the other. It is in orbit around a fixed point charge $+Q_{1}$. (The ends of the dipole are constrained to remain in the orbital plane.) Figure 1.57 shows the definitions of the coordinates $r, \theta, lpha$. Figu...
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72
<image>A pinhole camera consists of a box in which an image is formed on the film plane which is a distance $P$ from a pinhole of diameter $d$. The object is at a distance $L$ from the pinhole, and light of wavelength $\nabla$ is used (Fig. 2.66). Approximately what diameter $d$ of the pinhole will give the best image ...
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73
<image>Figure 1.24 is an energy level diagram for the ground state and first four excited states of a helium atom. Given electrons of sufficient energy, which levels could be populated as the result of electrons colliding with ground state atoms?
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74
<image><image>What are the neutron separation energies for ${ }_{20}^{40}\text{Ca}$ and ${ }_{82}^{208}\text{Pb}$ ?
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75
<image><image>Consider the Babinet Compensator shown in the figure (Fig.~2.76). The device is constructed from two pieces of uniaxial optical material with indices $n_{e}$ and $n_{o}$ for light polarized perpendicular and parallel to the optic axis, respectively. A narrow beam of light of vacuum wavelength $\lambda$ is...
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76
<image>A very long conducting pipe has a square cross section of its inside surface, with side $D$ as in Fig. 1.47. Far from either end of the pipe is suspended a point charge located at the center of the square cross section. Give the asymptotic expression for this potential for points far from the point charge.
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77
<image>The space between two long thin metal cylinders is filled with a material with dielectric constant $\varepsilon$. The cylinders have radii $a$ and $b$, as shown in Fig. 1.19. What is the electric field between the cylinders?
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78
<image>A particle of mass m is released at $t=0$ in the one-dimensional double square well shown in the figure in such a way that its wave function at $t=0$ is just one sinusoidal loop (half a sine wave with nodes just at the edges of the left half of the potential as shown). Find the average value of the energy at $t=...
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79
<image>Inelastic neutrino scattering in the quark model. Consider the scattering of neutrinos on free, massless quarks. We will simplify things and discuss only strangeness‐conserving reactions, i.e. transitions only between the $u$ and $d$ quarks. Assume that inelastic $u$ (or $\bar{u}$)-nucleon cross sections are giv...
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80
<image>Three identical objects, each of mass $m$, are connected by springs of spring constant $K$, as shown in Fig. 1.95. The motion is confined to one dimension. At $t=0$, the masses are at rest at their equilibrium positions. Mass $A$ is then subjected to an external time‐dependent driving force $F(t)=f \cos(\omega t...
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81
<image>A simple molecular beam apparatus is shown in Fig. 2.40. The oven contains $\mathrm{H}_{2}$ molecules at 300 K and at a pressure of 1 mm of mercury. The hole on the oven has a diameter of $100 \mu \mathrm{~m}$ which is much smaller than the molecular mean free path. After the collimating slits, the beam has a di...
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82
<image>Figure 2.19 gives the low-lying states of ${}^{18}\text{O}$ with their spin-parity assignments and energies (in MeV) relative to the $0^{+}$ ground state. What $J^{p}$ values are expected for the low-lying states of ${}^{19}\text{O}$?
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83
<image>Consider a $2-\text{cm}$ thick plastic scintillator directly coupled to the surface of a photomultiplier with a gain of $10^{6}$. A $10-\text{GeV}$ particle beam is incident on the scintillator as shown in Fig. 4.8(a). Suppose one could detect a signal on the anode of as little as $10^{-12}$ coulomb. If the beam...
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84
<image><image><image><image>Suppose you have been supplied with a number of sheets of two types of optically active material. Sheets of type $P$ are perfect polarizers: they transmit (normally incident) light polarized parallel to some axis $\boldsymbol{n}$ and absorb light polarized perpendicular to $\boldsymbol{n}$. ...
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85
<image>In an experiment a beam of silver atoms emerges from an oven, which contains silver vapor at $T=1200 \, \mathrm{K}$. The beam is collimated by being passed through a small circular aperture. If the screen is at $L=1$ meter from the aperture, estimate numerically the smallest $D$ that can be obtained by varying $...
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86
<image>The pions that are produced when protons strike the target at Fermilab are not all moving parallel to the initial proton beam. A focusing device, called a "horn", (actually two of them are used as a pair) is used to deflect the pions so as to cause them to move more closely towards the proton beam direction. Thi...
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87
<image>In Fig. 3.70 the circuit is a "typical" TTL totom pole output circuit. You should assume that all the solid state devices are silicon unless you specifically state otherwise. Give the voltages requested within 0.1 volt. Case 2: $V_{\mathrm{A}}=0.2$ volts, give $V_{\mathrm{B}}, V_{\mathrm{C}}, V_{\mathrm{D}}, V_{...
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88
<image>A thin spherical shell of radius $R$ has a fixed charge $+q$ distributed uniformly over its surface. A small circular section (radius $r \ll R$) of charge is removed from the surface. The cut section is replaced and the sphere is set in motion rotating with constant angular velocity $\omega=\omega_{0}$ about the...
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89
<image>A circular aperture of radius $a$ is uniformly illuminated by plane waves of wavelength $\lambda$. Let the $\boldsymbol{z}$-axis coincide with the aperture axis, with $z=0$ at the aperture, and with the incident flux travelling from negative values of $z$ toward $z=0$ (Fig.~2.30). Find the values of $z$ at which...
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90
<image>The Stark effect. The energy levels of the $n=2$ states of atomic hydrogen are illustrated in Fig. 5.14. The $S_{1/2}$ and $P_{1/2}$ levels are degenerate at an energy $\varepsilon_{0}$ and the $P_{3/2}$ level is degenerate at an energy $\varepsilon_{0}+A$. A uniform static electric field $E$ applied to the atom...
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91
<image>A flyball governor consists of two masses $m$ connected to arms of length $l$ and a mass $M$ as shown in Fig. 2.68. The assembly is constrained to rotate around a shaft on which the mass $M$ can slide up and down without friction. Neglect the mass of the arms, air friction, and assume that the diameter of the ma...
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92
<image>A ray of light enters a spherical drop of water of index $n$ as shown (Fig. 1.21). Find an expression for the angle of deflection $\delta$.
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93
<image>Consider a $2-\text{cm}$ thick plastic scintillator directly coupled to the surface of a photomultiplier with a gain of $10^{6}$. A $10-\text{GeV}$ particle beam is incident on the scintillator as shown in Fig. 4.8(a). Same as Part (b), but it scatters elastically from a carbon nucleus.
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94
<image>For the combination of one prism and 2 lenses shown (Fig. 1.42), find the location and size of the final image when the object, length 1 cm, is located as shown in the figure.
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95
<image>Looking through a small hole is a well-known method to improve sight. If your eyes are near-sighted and can focus an object 20 cm away without using any glasses, estimate the required diameter of the hole through which you would have good sight for objects far away.
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96
<image>In Fig. 2.71, the cylindrical cavity is symmetric about its long axis. For the purposes of this problem, it can be approximated as a coaxial cable (which has inductance and capacitance) shorted at one end and connected to a parallel plate disk capacitor at the other. Derive an expression for the lowest resonant ...
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97
<image>For the circuit shown in Fig. 3.35, the coupling coefficient of mutual inductance for the two coils $L_{1}$ and $L_{2}$ is unity. What is the average power supplied by the oscillator as a function of frequency?
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98
<image>A sound field is created by an arrangement of identical line sources grouped into two identical arrays of $N$ sources each as shown (Fig. 2.62) below.\nAll of the radiators lie in a plane perpendicular to the page, and produce waves of wavelength $\theta, N, c$ and $d$, the distance between the centers of the ar...
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99
<image><image><image><image>Any linear dc network (a load $R$ is connected between the two arbitrary points A and B of the network) is equivalent to a series circuit consisting of a battery of emf $V$ and a resistance $r$, as shown in Fig. 3.4. Calculate $V$ and $r$ of the circuit in Fig. 3.6. (Hint: Use mathematical i...
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