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900
<image>半径为 $R$ 的平面圆形线圈中载有电流 $I_{2}$ ，另一无限长直导线 $AB$ 中载有电流 $I_{1}$ ，若 $AB$ 与圆心相距 $d (d>R)$ ，仍在同一平面内，求圆形线圈所受的磁场力。
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901
<image>在载有电流 $I_{1}$ 的长直导线的磁场中，放置一等腰直角三角形线圈，直角边长为 $a$，通有电流 $I_{2}$。开始时线圈和长直导线在同一平面内，如习题8－49图所示。保持电流 $I_{1}$ 和 $I_{2}$ 不变而将线圈绕 $A B$ 边转动 $180^{\circ}$，试求转动过程中磁力所做的功。
[ -0.0000400543212890625, -0.006256103515625, 0.000640869140625, -0.0089111328125, 0.01397705078125, 0.015869140625, -0.004730224609375, -0.002777099609375, -0.033203125, -0.018798828125, -0.056884765625, 0.01239013671875, -0.011474609375, -0.0233154296875, 0.031494140625, -0.01599121093...
902
<image>在载有电流 $I_{1}$ 的长直导线的磁场中，放置一等腰直角三角形线圈，直角边长为 $a$，通有电流 $I_{2}$。开始时线圈和长直导线在同一平面内，如习题8－49图所示。保持电流 $I_{1}$ 和 $I_{2}$ 不变而将线圈绕 $B C$ 边转动 $180^{\circ}$，试求转动过程中磁力所做的功。
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903
<image>两根长直导线互相平行地放置在真空中，如图所示，其中通以同向的电流 $I_{1}=I_{2}=10 \mathrm{~A}$ 。试求 $P$ 点的磁感应强度。已知 $P$ 点到两导线的垂直距离均为 0.5 m 。
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904
<image>如图所示，$PQ$ 和 $MN$ 为两根金属棒，各长 1 m ，电阻都是 $R=4\Omega$，放置在均匀磁场中，已知 $B=2\mathrm{~T}$，方向垂直纸面向里。当两根金属棒在导轨上分别以 $v_{1}=4\mathrm{~m/s}$ 和 $v_{2}=2\mathrm{~m/s}$ 的速度向左运动时，忽略导轨的电阻，试求：金属棒两端的电势差 $U_{PO}$ 。
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905
<image>如图所示，$PQ$ 和 $MN$ 为两根金属棒，各长 1 m ，电阻都是 $R=4\Omega$，放置在均匀磁场中，已知 $B=2\mathrm{~T}$，方向垂直纸面向里。当两根金属棒在导轨上分别以 $v_{1}=4\mathrm{~m/s}$ 和 $v_{2}=2\mathrm{~m/s}$ 的速度向左运动时，忽略导轨的电阻，试求：金属棒两端的电势差 $U_{MN}$ 。
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906
<image>在半径为 $a$ 的无限长圆柱空间内，均匀磁场随时间增大，即 $\frac{\mathrm{d} B}{\mathrm{~d} t}>0$ 。等腰梯形线框 $A B C D$ ，上底长为 $a$ ，下底长为 $2 a$ ，放置如图所示。试求线框各边上的感应电动势
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907
<image>在半径为 $a$ 的无限长圆柱空间内，均匀磁场随时间增大，即 $\frac{\mathrm{d} B}{\mathrm{~d} t}>0$ 。等腰梯形线框 $A B C D$ ，上底长为 $a$ ，下底长为 $2 a$ ，放置如图所示。试求整个线框中的感应电动势
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908
<image>一截面为长方形的螺绕管，其尺寸如图所示，共有 $N$ 匝，求此螺绕管的自感。
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909
<image>将金属薄片弯成如图所示形状的器件，两侧是半径为 $a$ 的圆柱，中间是边长为 $l$ ，间隔为 $d$ 的两正方形的平面，且 $l \gg a, a \gg d$ 。试求该器件的自感系数。
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910
<image>一矩形线圈长 $l=20\,\mathrm{cm}$，宽 $b=10\,\mathrm{cm}$，由 100 匝表面绝缘的导线绕成，放置在一根长直导线的旁边，并和直导线在同一平面内，该长直导线是一个闭合回路的一部分，其余部分离线圈很远，其影响可略去不计。求习题 9－24 图（b）情况下，线圈与长直导线间的互感。
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911
<image>两个圆线圈 A 和 B ，半径分别为 $a$ 和 $b$ ，且 $b \gg a$ ，共轴放置，两线圈中心相距为 $l(l \gg b)$ ，如图所示。今在小线圈中通有电流 $I=I_{0}\mathrm{e}^{\lambda t} (\lambda>0)$ 。求大线圈中的感应电动势。（提示：先求出两线圈的互感系数。）
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912
<image>一同轴电缆，由半径为 $a$ 的导体圆柱芯线及内，外半径分别为 $b$ 和 $c$ 的同轴导体圆筒组成，如图所示。筒与柱间有相对磁导率为 $\mu_{\mathrm{r}}$ 的磁介质，导体圆柱和圆筒的磁导率近似为 $\mu_{0}$ 。电缆工作时，电流由圆柱流入，沿圆筒济回，而且在导体横截面上电流是均匀分布的。并由此计算电缆单位长度的自感。
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913
<image>一无限长直导线与一矩形线框处在同一平面内，彼此绝缘，如习题 9－2图所示。若直导线中通有电流 $I=A t$, $A$ 为正值常量，试求此线框中的感应电动势的大小。
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914
<image>点电荷 $+q$ 以速度 $\boldsymbol{v}(v \ll c)$ 作匀速直线运动，试从位移电流得到运动电荷的磁场的关系式。（提示：当电荷低速运动时，可以认为电荷周围的电场仍保持球对称分布。电荷在运动，电场在变化，所以产生磁场。以点电荷为球心，过场点 $P$ 作球面，求出通过截面圆的 $D$ 通量，如图所示）
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915
<image>如果改变自感 $L$ 的大小，金属杆的运动速度及线圈内电流将如何变化？
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916
<image>在长直导线旁有一导体线框，两者在同一平面内，线框中 $cd$ 段可以自由滑动，如图所示。设导线中的电流 $I=I_{0}\mathrm{e}^{-\lambda t}$ $(\lambda>1)$ 。开始时，导线 $cd$ 在线框的最左端，以速度 $v$ 向右匀速滑动。试求线框中的感应电动势。（忽略线框中的感应电流对磁场的影响）
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917
<image>长直导线与直角三角形线圈共面放置，如图所示。若直导线中通有恒定电流 $I$ ，线圈以速度 $v$ 向右平动。求直边 $l_{A B}$ 上的感应电动势。
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918
<image>长直导线与直角三角形线圈共面放置，如图所示。若直导线中通有恒定电流 $I$ ，线圈以速度 $v$ 向右平动。求斜边 $l_{B C}$ 上的感应电动势。
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919
<image>长直导线与直角三角形线圈共面放置，如图所示。若直导线中通有恒定电流 $I$ ，线圈以速度 $v$ 向右平动。求线圈的总感应电动势。
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920
<image><image>The digital transmission of speech may be represented using the block diagram of Fig. 6.1. Part of the signal at point $P$ on Fig. 6.1 is shown in Fig. 6.2. The analogue-to-digital converter (ADC) samples the signal at time intervals of 0.25 ms . Each sample is converted into a four-bit number with the sm...
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921
<image><image>A solenoid of diameter $6.0\,\rm{cm}$ and 540 turns is placed in a uniform magnetic field as shown in Fig. 9.1. The variation with time $t$ of the magnetic flux density is shown in Fig. 9.2. Calculate the maximum magnitude of the induced electromotive force (e.m.f.) in the solenoid. e.m.f. = V
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922
<image><image><image>A thin copper sheet $X$ is supported on a rigid rod so that it hangs between the poles of a magnet as shown in Fig. 9.3. Sheet $X$ is displaced to one side and then released so that it oscillates. A motion sensor is used to record the displacement of $X$. A second thin copper sheet $Y$ replaces she...
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923
<image><image>Polonium-211 $({ }_{84}^{211} \mathrm{Po})$ decays by alpha emission to form a stable isotope of lead $(\mathrm{Pb})$. Each decay releases an alpha particle with energy 6900 keV. Calculate, in J, the total amount of energy given to alpha particles that are emitted between time $t=0.30\,\mathrm{s}$ and tim...
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924
<image>Artemis is a spherical planet that may be assumed to be isolated in space. The variation with distance $x$ from the centre of Artemis of the gravitational potential $\phi$ is shown in Fig. 1.1. The radius of Artemis is 4800 km. Determine the value of $\phi$ on the surface of Artemis.
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925
<image>Artemis is a spherical planet that may be assumed to be isolated in space. The variation with distance $x$ from the centre of Artemis of the gravitational potential $\phi$ is shown in Fig. 1.1. The radius of Artemis is 4800 km. Calculate the gravitational field strength $g$ on the surface of Artemis.
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926
<image>A Hall probe gives a maximum reading of 24 mV when placed in a uniform magnetic field of flux density 32 mT. The same Hall probe is then placed in a magnetic field of fixed direction and varying flux density. The Hall probe is in a fixed position so that the angle between the Hall probe and the magnetic field is...
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927
<image><image>A bar magnet of mass 250 g is suspended from the free end of a spring, as illustrated in Fig. 3.1. The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed t...
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928
<image><image>Two charged metal spheres $A$ and $B$ are situated in a vacuum, as illustrated in Fig. 6.1. The shortest distance between the surfaces of the spheres is 6.0 cm. A movable point $P$ lies along the line joining the centres of the two spheres, a distance $x$ from the surface of sphere $A$. The variation with...
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929
<image>An ideal op-amp is incorporated into the amplifier circuit shown in Fig. 8.1. Determine the output potential difference $V_{\text{OUT}}$ for input potential differences $V_{\text{IN}}$ of $+1.3\text{ V}$.
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930
<image>The variation with time $t$ of the number $N$ of technetium-101 nuclei in a sample of radioactive material is shown in Fig. 13.1. Use Fig. 13.1 to determine the activity, in Bq, of the sample of technetium-101 at time $t=14.0$ minutes.
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931
<image>An ideal operational amplifier (op-amp) is incorporated into the circuit shown in Fig. 7.1. Determine the output potential difference $V_{\text{OUT}}$ for an input potential difference $V_{\text{IN}}$ of -2.1 V.
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932
<image><image>A metal sphere of radius $R$ is isolated in space. Point $P$ is a distance $x$ from the centre of the sphere, as illustrated in Fig. 7.1. The variation with distance $x$ of the electric field strength $E$ due to the charge on the sphere is shown in Fig. 7.2. Use Fig. 7.2 to determine the radius $R$ of the...
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933
<image>A uniform electric field is now applied in the same region as the magnetic field. The electron passes undeviated through the region of the two fields, as illustrated in Fig. 9.2. The speed of the electron is $9.0 \times 10^{6}\,\mathrm{ms}^{-1}$. Calculate the magnitude of the electric field strength.
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934
<image>The accelerated electrons are injected at point S into a region of uniform magnetic field of flux density $B$, as illustrated in Fig. 8.1. The electrons move at right angles to the direction of the magnetic field. The path of the electrons is a circle of radius $r$. Calculate the specific charge $\frac{q}{m}$ of...
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935
<image>An X-ray image is taken of the structure shown in Fig. 9.1. The linear attenuation coefficient of bone is $3.4 \mathrm{~cm}^{-1}$. The linear attenuation coefficient of soft tissue is $0.89 \mathrm{~cm}^{-1}$. The incident X-rays are parallel and have a uniform intensity $I_{0}$ across the structure. Determine, ...
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936
<image>Fig. 10.1 shows the wavelength distributions of electromagnetic radiation emitted by two stars $A$ and $B$. The surface temperature of star $A$ is known to be 5800 K. Determine the surface temperature of star B.
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937
<image><image>A steel sphere of mass 0.29 kg is suspended in equilibrium from a vertical spring. The centre of the sphere is 8.5 cm from the top of the spring, as shown in Fig. 2.1. The sphere is now set in motion so that it is moving in a horizontal circle at constant speed, as shown in Fig. 2.2. The distance from the...
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938
<image>A beaker contains a liquid of mass 120 g. The liquid is supplied with thermal energy at a rate of 810 W. The beaker has a mass of 42 g and a specific heat capacity of $0.84 \mathrm{Jg}^{-1} \mathrm{K}^{-1}$. The beaker and the liquid are in thermal equilibrium with each other at all times and are insulated from ...
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939
<image><image>Fig. 8.1 shows the lowest four energy levels of an electron in an isolated atom. Fig. 8.2 shows the lines in the emission spectrum of the atom that correspond to the transitions of the electron from $n=3$ to $n=1$ and from $n=4$ to $n=1$. (c) The frequency of radiation represented by line $A$ is $f_{A}$. ...
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940
<image>An isolated spherical conductor has charge $q$, as shown in Fig. 6.1. Point $P$ is a movable point that, at any one time, is a distance $x$ from the centre of the sphere. The variation with distance $x$ of the electric potential $V$ at point $P$ due to the charge on the sphere is shown in Fig. 6.2. Use Fig. 6.2 ...
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941
<image>The variation with time $t$ of the displacement $x$ is shown in Fig. 3.3. The period of oscillation of the liquid column of mass 18.0 g is $T$. The oscillations are damped. Calculate the loss in total energy of the oscillations during the first 2.5 periods of the oscillations.
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942
<image>An incomplete circuit for a non-inverting amplifier incorporating an ideal operational amplifier is shown in Fig. 7.1. The completed amplifier of Fig. 7.1 has a voltage gain of 10. State the output voltage $V_{\text{OUT}}$ for an input voltage $V_{\text{IN}}$ of 0.56 V.
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943
<image><image><image>A student determines the specific latent heat of vaporisation of a liquid using the apparatus illustrated in Fig. 3.1. The heater is switched on. When the liquid is boiling at a constant rate, the balance reading is noted at 2.0 minute intervals. After 10 minutes, the current in the heater is reduc...
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944
<image><image><image>A student determines the specific latent heat of vaporisation of a liquid using the apparatus illustrated in Fig. 3.1. The heater is switched on. When the liquid is boiling at a constant rate, the balance reading is noted at 2.0 minute intervals. After 10 minutes, the current in the heater is reduc...
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945
<image><image><image>A student determines the specific latent heat of vaporisation of a liquid using the apparatus illustrated in Fig. 3.1. The heater is switched on. When the liquid is boiling at a constant rate, the balance reading is noted at 2.0 minute intervals. After 10 minutes, the current in the heater is reduc...
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946
<image><image><image>A mass is suspended vertically from a fixed point by means of a spring, as illustrated in Fig. 4.1. The mass is oscillating vertically. The variation with displacement $x$ of the acceleration $a$ of the mass is shown in Fig. 4.2. (b)(i) State the maximum amplitude $x_{0}$ for which the oscillations...
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947
<image><image><image>A mass is suspended vertically from a fixed point by means of a spring, as illustrated in Fig. 4.1. The mass is oscillating vertically. The variation with displacement $x$ of the acceleration $a$ of the mass is shown in Fig. 4.2. (b)(ii) For the simple harmonic oscillations of the mass, use Fig. 4....
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948
<image>The input power of the signal to the transmission cable is 2.6 W. The attenuation per unit length of the cable is $6.3 \mathrm{~dB} \mathrm{~km}^{-1}$. Use your answer in (i) to determine the maximum uninterrupted length $L$ of cable along which the signal may be transmitted.
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949
<image><image><image>A student uses the apparatus illustrated in Fig. 3.1 to determine a value for the specific latent heat of fusion of ice. The balance reading measures the mass of the beaker and the melted ice (water) in the beaker. The heater is switched on and pieces of ice at $0^{\circ}\mathrm{C}$ are added conti...
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950
<image><image>The variation with time of the displacement of an amplitude-modulated (AM) wave is shown in Fig. 6.1. The sinusoidal information signal has frequency 10 kHz. Determine the frequency of the carrier wave.
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951
<image>The force on the electrons causes a voltage $V_{H}$ to be established across the semiconductor slice given by the expression $V_{\mathrm{H}}=\frac{B I}{n t q}$ where $I$ is the current in the slice. State the two faces between which the voltage $V_{H}$ is established.
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952
<image>The force on the electrons causes a voltage $V_{H}$ to be established across the semiconductor slice given by the expression $V_{\mathrm{H}}=\frac{B I}{n t q}$ where $I$ is the current in the slice. Use letters from Fig. 8.1 to identify the distance $t$.
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953
<image><image><image>A comparator circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 10.2. The variation with temperature $\theta$ of the resistance $R_{\mathrm{T}}$ of the thermistor is shown in Fig. 10.3. Determine the temperature at which the light-emitting diode (LED) in Fig. 10.2 switch...
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954
<image><image>A pendulum consists of a metal sphere $P$ suspended from a fixed point by means of a thread, as illustrated in Fig. 3.1. The centre of gravity of sphere $P$ is a distance $L$ from the fixed point. The sphere is pulled to one side and then released so that it oscillates. The sphere may be assumed to oscill...
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955
<image><image>A pendulum consists of a metal sphere $P$ suspended from a fixed point by means of a thread, as illustrated in Fig. 3.1. The centre of gravity of sphere $P$ is a distance $L$ from the fixed point. The sphere is pulled to one side and then released so that it oscillates. The sphere may be assumed to oscill...
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956
<image>Two point charges $A$ and $B$ are separated by a distance of 12.0 cm in a vacuum, as illustrated in Fig. 5.1. The charge of $A$ is $+2.0 \times 10^{-9} \mathrm{C}$. A point $P$ lies on the line joining charges $A$ and $B$. Its distance from charge $A$ is $x$. The variation with distance $x$ of the electric poten...
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957
<image>A student has available four capacitors, each of capacitance $24 \mu \mathrm{~F}$. The capacitors are connected as shown in Fig. 6.1. Calculate the combined capacitance between the terminals X and Y .
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958
<image>The maximum kinetic energy $E_{\text{MAX}}$ of electrons emitted from a metal surface is determined for different wavelengths $\lambda$ of the electromagnetic radiation incident on the surface. The variation with $\frac{1}{\lambda}$ of $E_{\mathrm{MAX}}$ is shown in Fig. 11.1. Use Fig. 11.1 to determine the thre...
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959
<image>The maximum kinetic energy $E_{\text{MAX}}$ of electrons emitted from a metal surface is determined for different wavelengths $\lambda$ of the electromagnetic radiation incident on the surface. The variation with $\frac{1}{\lambda}$ of $E_{\mathrm{MAX}}$ is shown in Fig. 11.1. Use the gradient of the line on Fig...
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960
<image>Fig. 6.1 shows a thin slice of semiconducting material used in a Hall probe. Current $I$ passes through the slice in the direction shown. The slice is placed in a uniform magnetic field of flux density $B$, so that two of its faces are perpendicular to the magnetic field. A steady Hall voltage $V_{H}$ is develop...
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961
<image><image>Fig. 4.1 shows the variation with time $t$ of the height $h$ above the ground of an object of mass 36 kg that is undergoing vertical simple harmonic motion. For the oscillations of the object: determine the total energy $E$
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962
<image>An isolated conducting sphere is charged. Fig. 5.1 shows the variation of the potential $V$ due to the sphere with displacement $x$ from its centre. Use Fig. 5.1 to determine: the radius of the sphere
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963
<image>An isolated conducting sphere is charged. Fig. 5.1 shows the variation of the potential $V$ due to the sphere with displacement $x$ from its centre. Use Fig. 5.1 to determine: the charge on the sphere.
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964
<image><image><image>A capacitor of capacitance $C$ and a resistor of resistance $R$ are connected as shown in Fig. 6.1. Initially, the capacitor is charged and the switch is open. The switch is closed at time $t=0$. Fig. 6.2 and Fig. 6.3 show, respectively, the variations with $t$ of the charge $Q$ on the capacitor an...
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965
<image>An alternating voltage of peak value 150 V is applied across the 1200 turns of the primary coil. The variation with time $t$ of the e.m.f. $E$ induced across the secondary coil is shown in Fig.9.2. Use data from Fig. 9.2 to calculate the number of turns of the secondary coil.
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966
<image>TESS is a satellite of mass 360 kg in a circular orbit about the Earth. The radius of the Earth is $6.4 \times 10^{6} \mathrm{~m}$ and the mass of the Earth, considered to be a point mass at its centre, is $6.0 \times 10^{24} \mathrm{~kg}$. Calculate the change in gravitational potential energy between TESS in o...
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967
<image>TESS is a satellite of mass 360 kg in a circular orbit about the Earth. The radius of the Earth is $6.4 \times 10^{6} \mathrm{~m}$ and the mass of the Earth, considered to be a point mass at its centre, is $6.0 \times 10^{24} \mathrm{~kg}$. Use the information in (b)(i) to calculate the ratio: $\frac{\text{gravi...
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968
<image>A body undergoes simple harmonic motion. The variation with displacement $x$ of its velocity $v$ is shown in Fig. 3.1. Calculate the period $T$ of the oscillations.
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969
<image>A beam of X-rays has an initial intensity $I_{0}$. The beam is directed into some body tissue. After passing through a thickness $x$ of tissue the intensity is $I$. The graph in Fig. 11.1 shows the variation with $x$ of $\ln\left(I/I_{0}\right)$. Determine the linear attenuation (absorption) coefficient $\mu$ fo...
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970
<image>The variation with radius $r$ of the electric field strength $E$ due to an isolated charged sphere in a vacuum is shown in Fig. 6.1. Use data from Fig. 6.1 to: state the radius of the sphere.
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971
<image>The variation with radius $r$ of the electric field strength $E$ due to an isolated charged sphere in a vacuum is shown in Fig. 6.1. Use data from Fig. 6.1 to: calculate the charge on the sphere.
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972
<image>The block is now placed in a liquid with a greater density. The block is displaced and released so that it oscillates vertically. The variation with displacement $x$ of the acceleration a of the block is measured for the first half oscillation, as shown in Fig. 3.3. The mass of the block is 0.57 kg. Use Fig. 3.3...
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973
<image>The output voltage $V$ of an a.c. power supply varies sinusoidally with time $t$ as shown in Fig. 7.2. The supply is connected to a $12\Omega$ resistor. Calculate the mean power dissipated in the resistor.
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974
<image><image>An object is suspended from a vertical spring as shown in Fig. 3.1.\n\nThe object is displaced vertically and then released so that it oscillates, undergoing simple harmonic motion.\n\nFig. 3.2 shows the variation with displacement $x$ of the energy $E$ of the oscillations.\nThe kinetic energy, the potent...
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975
<image><image>A bar magnet of mass 180 g is suspended from the free end of a spring, as illustrated in Fig. 2.1. The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed t...
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976
<image><image>A trolley of mass 950 g is held on a horizontal surface by means of two springs attached to fixed points $P$ and $Q$, as shown in Fig. 4.1. The springs, each having a spring constant $k$ of $230 \mathrm{Nm}^{-1}$, are always extended. The trolley is displaced along the line of the springs and then release...
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977
<image><image>A bridge rectifier contains four diodes. The output of the rectifier is connected to a resistor $R$, as shown in Fig. 10.1.\n\nThe variation with time $t$ of the input e.m.f. $E$ to the rectifier is given by the expression\n$$E=15 \cos (210 t)$$\nwhere $t$ is measured in seconds and $E$ in volts.\nThe var...
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978
<image><image>The variation with temperature $t$ of the resistance $R$ of a thermistor is shown in Fig. 7.1. The thermistor is connected into the circuit shown in Fig. 7.2. The battery has electromotive force (e.m.f.) 9.00 V and negligible internal resistance. When the temperature of the thermistor is $25^{\circ} \math...
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979
<image><image>A metal sphere of radius $R$ is isolated in space. Point $P$ is a distance $x$ from the centre of the sphere, as illustrated in Fig. 7.1. The variation with distance $x$ of the electric field strength $E$ due to the charge on the sphere is shown in Fig. 7.2. Use Fig. 7.2 to determine the charge $Q$ on the...
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980
<image><image>The gas undergoes three successive changes, as shown in Fig. 3.1. The initial state is represented by point $A$. The gas is cooled at constant pressure to point $B$ by the removal of 48.0 kJ of thermal energy. The gas is then heated at constant volume to point $C$. Finally, the gas expands at constant tem...
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981
<image><image><image>Fig. 5.2 shows the variation with time $t$ of $V_{\mathbb{IN}}$ and Fig. 5.3 shows the variation with $t$ of $V_{\text{OUT}}$. Calculate the time constant $\tau$ for the discharge of the capacitor through the resistor.
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982
<image><image><image>Fig. 5.2 shows the variation with time $t$ of $V_{\mathbb{IN}}$ and Fig. 5.3 shows the variation with $t$ of $V_{\text{OUT}}$. Calculate the capacitance of $C$. Give a unit with your answer.
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983
<image><image>A second long, straight wire $Q$, carrying a current of5.0 A out of the page, is placed parallel to wire $P$, as shown in Fig. 6.2. (The flux density of the magnetic field at wire $P$ due to the current in wire $Q$ is 1.5 mT. Determine the magnitude of the current in wire $P$.
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984
<image>A thin metal strip is clamped at one end so that it is horizontal. A load of mass $M$ is attached to its free end. The load causes a displacement $s$ of the end of the strip, as shown in Fig. 2.1. The load is displaced vertically and then released. The load oscillates. The variation with the acceleration $a$ of ...
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985
<image>The lowest electron energy levels in an isolated hydrogen atom are shown in Fig. 11.1. Photons resulting from electron de-excitation from the $-0.85\,\text{eV}$ energy level are incident on the surface of a sample of platinum. Platinum has a work function energy of $5.6\,\text{eV}$. Determine the maximum kinetic...
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986
<image><image><image>A student uses the apparatus illustrated in Fig. 3.1 to determine a value for the specific latent heat of fusion of ice. The balance reading measures the mass of the beaker and the melted ice (water) in the beaker. The heater is switched on and pieces of ice at $0^{\circ}\mathrm{C}$ are added conti...
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987
<image><image>One section of a model designed to illustrate CT scanning is divided into four voxels. The pixel numbers $K$, $L$, $M$ and N of the voxels are shown in Fig. 10.1. The section is viewed, in turn, from four different directions $D_{1}$, $D_{2}$, $D_{3}$ and $D_{4}$, as shown in Fig. 10.1. The detector readi...
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988
<image>A sample of radioactive material contains atoms of an unstable nuclide $X$. The activity of the sample due to the atoms of $X$ is $A$. The variation with time $t$ of $\ln A$ is shown in Fig. 12.1. At time $t=0$, the mass of the atoms of $X$ in the sample is $5.66 \times 10^{-7} \mathrm{~kg}$. Determine the nucle...
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989
<image><image><image>A capacitor of capacitance $C$ and a resistor of resistance $R$ are connected as shown in Fig. 6.1. Initially, the capacitor is charged and the switch is open. The switch is closed at time $t=0$. Fig. 6.2 and Fig. 6.3 show, respectively, the variations with $t$ of the charge $Q$ on the capacitor an...
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990
<image>One possible path of the spacecraft as it approaches the planet is shown in Fig. 1.1. The spacecraft enters the orbit at point A with speed $3.7 \times 10^{3} \mathrm{~ms}^{-1}$. At point $B$, a distance of $5.00 \times 10^{7} \mathrm{~m}$ from the centre of the planet, the spacecraft has a speed of $4.1 \times ...
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991
<image><image>A dish is made from a section of a hollow glass sphere. The dish, fixed to a horizontal table, contains a small solid ball of mass 45 g, as shown in Fig. 4.1. The horizontal displacement of the ball from the centre $C$ of the dish is $x$. Initially, the ball is held at rest with distance $x=3.0\,\mathrm{c...
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992
<image>For the solenoids shown in the diagram (which are assumed to be close to each other), the resistance of the left-hand circuit is slowly increased. In which direction does the galvanometer needle in the right-hand circuit move in response to this change?
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993
<image>An object on an inclined plane has a gravitational force of magnitude $10$ N acting on it from the Earth. What are the correct components of this gravitational force for the coordinate axes where the $y$-axis is perpendicular to the incline's surface and the $x$-axis is parallel to the inclined surface?
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994
<image>A uniform meter stick has a 45.0 g mass placed at the 20 cm mark as shown in the figure. If a pivot is placed at the 42.5 cm mark and the meter stick remains horizontal in static equilibrium, what is the mass of the meter stick?
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995
<image>An infinitely long solenoid passes through the circuit as shown. The magnetic field of the solenoid, directed into the plane of the page, is weakening which produces a constant emf of magnitude $\xi$ for a closed loop around the outside of the solenoid. Once equilibrium is established in this circuit, what is th...
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996
<image>What is the average speed of the car for the 10 second interval?
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997
<image>Astronauts on the Moon perform an experiment with a simple pendulum that is released from the horizontal position at rest. At the moment shown in the diagram with $0^{\circ}<\theta<90^{\circ}$, in which direction may the total acceleration of the mass be directed?
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998
<image>A spatially uniform electric field is constrained within the circular region of radius $R$ as shown. The field is directed out of the plane of the page and its strength is increasing uniformly in time. What is the direction of the force on the proton in the figure if the proton is moving to the right at the inst...
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999
<image>In the figure to the right, a box moves with speed $5.00 \, \mathrm{m/s}$ at the bottom of a rough, fixed inclined plane and is pushed directly to the left with a constant force of $F=240 \, \mathrm{N}$. The box, of mass $m=20.0 \, \mathrm{kg}$, has a speed of $2.50 \, \mathrm{m/s}$ when it reaches the top of th...
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