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When calculating potential and current using Kirchhoffâs rules, a set of conventions must be followed for determining the correct signs of various terms. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
When multiple voltage sources are in series, their internal resistances add together and their emfs add together to get the total values. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
When multiple voltage sources are in parallel, their internal resistances combine to an equivalent resistance that is less than the individual resistance and provides a higher current than a single cell. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Solar cells can be wired in series or parallel to provide increased voltage or current, respectively. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Voltmeters measure voltage, and ammeters measure current. Analog meters are based on the combination of a resistor and a galvanometer, a device that gives an analog reading of current or voltage. Digital meters are based on analog-to-digital converters and provide a discrete or digital measurement of the current or vol... | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
A voltmeter is placed in parallel with the voltage source to receive full voltage and must have a large resistance to limit its effect on the circuit. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
An ammeter is placed in series to get the full current flowing through a branch and must have a small resistance to limit its effect on the circuit. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Standard voltmeters and ammeters alter the circuit they are connected to and are thus limited in accuracy. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Ohmmeters are used to measure resistance. The component in which the resistance is to be measured should be isolated (removed) from the circuit. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
AnRCcircuit is one that has both a resistor and a capacitor. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
The time constantÏÏfor anRCcircuit isÏ=RC.Ï=RC. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
When an initially uncharged(q=0att=0)(q=0att=0)capacitor in series with a resistor is charged by a dc voltage source, the capacitor asymptotically approaches the maximum charge. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
As the charge on the capacitor increases, the current exponentially decreases from the initial current:I0=ε/R.I0=ε/R. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
If a capacitor with an initial chargeQis discharged through a resistor starting att=0t=0, then its charge decreases exponentially. The current flows in the opposite direction, compared to when it charges, and the magnitude of the charge decreases with time. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
The two types of electric hazards are thermal (excessive power) and shock (current through a person). Electrical safety systems and devices are employed to prevent thermal and shock hazards. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Shock severity is determined by current, path, duration, and ac frequency. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
Circuit breakers and fuses interrupt excessive currents to prevent thermal hazards. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
The three-wire system guards against thermal and shock hazards, utilizing live/hot, neutral, and ground wires, and grounding the neutral wire and case of the appliance. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
A ground fault circuit interrupter (GFCI) prevents shock by detecting the loss of current to unintentional paths. | https://openstax.org/books/university-physics-volume-2/pages/10-summary |
F â = q v â Ã B â F â = q v â Ã B â | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
F = q v B sin θ F = q v B sin θ | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
r = m v q B r = m v q B | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
T = 2 Ï m q B T = 2 Ï m q B | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
F â = I l â Ã B â F â = I l â Ã B â | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
μ â = N I A n ^ μ â = N I A n ^ | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
Ï â = μ â à B â Ï â = μ â à B â | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
U = â μ â · B â U = â μ â · B â | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
v d = E B v d = E B | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
V = I B l n e A V = I B l n e A | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
V = B l v d V = B l v d | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
q m = E B B 0 R q m = E B B 0 R | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
v max = q B R m v max = q B R m | https://openstax.org/books/university-physics-volume-2/pages/11-key-equations |
cosmic rays : comprised of particles that originate mainly from outside the solar system and reach Earth | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
cyclotron : device used to accelerate charged particles to large kinetic energies | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
dees : large metal containers used in cyclotrons that serve contain a stream of charged particles as their speed is increased | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
gauss : G, unit of the magnetic field strength;1G=10â4T1G=10â4T | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
Hall effect : creation of voltage across a current-carrying conductor by a magnetic field | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
helical motion : superposition of circular motion with a straight-line motion that is followed by a charged particle moving in a region of magnetic field at an angle to the field | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
magnetic dipole : closed-current loop | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
magnetic dipole moment : termIAof the magnetic dipole, also calledμμ | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
magnetic field lines : continuous curves that show the direction of a magnetic field; these lines point in the same direction as a compass points, toward the magnetic south pole of a bar magnet | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
magnetic force : force applied to a charged particle moving through a magnetic field | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
mass spectrometer : device that separates ions according to their charge-to-mass ratios | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
motor (dc) : loop of wire in a magnetic field; when current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a shaft; electrical energy is converted into mechanical work in the process | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
north magnetic pole : currently where a compass points to north, near the geographic North Pole; this is the effective south pole of a bar magnet but has flipped between the effective north and south poles of a bar magnet multiple times over the age of Earth | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
right-hand rule-1 : using your right hand to determine the direction of either the magnetic force, velocity of a charged particle, or magnetic field | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
south magnetic pole : currently where a compass points to the south, near the geographic South Pole; this is the effective north pole of a bar magnet but has flipped just like the north magnetic pole | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
tesla : SI unit for magnetic field: 1 T = 1 N/A-m | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
velocity selector : apparatus where the crossed electric and magnetic fields produce equal and opposite forces on a charged particle moving with a specific velocity; this particle moves through the velocity selector not affected by either field while particles moving with different velocities are deflected by the appar... | https://openstax.org/books/university-physics-volume-2/pages/11-key-terms |
Magnets have two types of magnetic poles, called the north magnetic pole and the south magnetic pole. North magnetic poles are those that are attracted toward Earthâs geographic North Pole. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Like poles repel and unlike poles attract. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Discoveries of how magnets respond to currents by Oersted and others created a framework that led to the invention of modern electronic devices, electric motors, and magnetic imaging technology. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Charges moving across a magnetic field experience a force determined byFâ=qvâÃBâ.Fâ=qvâÃBâ.The force is perpendicular to the plane formed byvâvâandBâ.Bâ. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The direction of the force on a moving charge is given by the right hand rule 1 (RHR-1): Sweep your fingers in a velocity, magnetic field plane. Start by pointing them in the direction of velocity and sweep towards the magnetic field. Your thumb points in the direction of the magnetic force for positive charges. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Magnetic fields can be pictorially represented by magnetic field lines, which have the following properties:The field is tangent to the magnetic field line.Field strength is proportional to the line density.Field lines cannot cross.Field lines form continuous, closed loops. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The field is tangent to the magnetic field line. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Field strength is proportional to the line density. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Field lines cannot cross. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Field lines form continuous, closed loops. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Magnetic poles always occur in pairs of north and southâit is not possible to isolate north and south poles. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
A magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radiusr=mvqB.r=mvqB. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The period of circular motion for a charged particle moving in a magnetic field perpendicular to the plane of motion isT=2ÏmqB.T=2ÏmqB. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Helical motion results if the velocity of the charged particle has a component parallel to the magnetic field as well as a component perpendicular to the magnetic field. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
An electrical current produces a magnetic field around the wire. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The directionality of the magnetic field produced is determined by the right hand rule-2, where your thumb points in the direction of the current and your fingers wrap around the wire in the direction of the magnetic field. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The magnetic force on current-carrying conductors is given byFâ=IlâÃBâFâ=IlâÃBâwhereIis the current andlis the length of a wire in a uniform magnetic fieldB. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The net force on a current-carrying loop of any plane shape in a uniform magnetic field is zero. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The net torque Ï on a current-carrying loop of any shape in a uniform magnetic field is calculated usingÏ=μâÃBâÏ=μâÃBâwhereμâμâis the magnetic dipole moment andBâBâis the magnetic field strength. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The magnetic dipole momentμμis the product of the number of turns of wireN, the current in the loopI, and the area of the loopAorμâ=NIAn^.μâ=NIAn^. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Perpendicular electric and magnetic fields exert equal and opposite forces for a specific velocity of entering particles, thereby acting as a velocity selector. The velocity that passes through undeflected is calculated byv=EB.v=EB. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
The Hall effect can be used to measure the sign of the majority of charge carriers for metals. It can also be used to measure a magnetic field. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
A mass spectrometer is a device that separates ions according to their charge-to-mass ratios by first sending them through a velocity selector, then a uniform magnetic field. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
Cyclotrons are used to accelerate charged particles to large kinetic energies through applied electric and magnetic fields. | https://openstax.org/books/university-physics-volume-2/pages/11-summary |
μ 0 = 4 Ï Ã 10 â7 T â m/A μ 0 = 4 Ï Ã 10 â7 T â m/A | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
d B = μ 0 4 Ï I d l sin θ r 2 d B = μ 0 4 Ï I d l sin θ r 2 | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B â = μ 0 4 Ï â« wire I d l â à r ^ r 2 B â = μ 0 4 Ï â« wire I d l â à r ^ r 2 | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B = μ 0 I 2 Ï R B = μ 0 I 2 Ï R | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
F l = μ 0 I 1 I 2 2 Ï r F l = μ 0 I 1 I 2 2 Ï r | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B = μ 0 I 2 R (at center of loop) B = μ 0 I 2 R (at center of loop) | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
â® B â · d l â = μ 0 I â® B â · d l â = μ 0 I | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B = μ 0 n I B = μ 0 n I | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B = μ o N I 2 Ï r B = μ o N I 2 Ï r | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
μ = ( 1 + Ï ) μ 0 μ = ( 1 + Ï ) μ 0 | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
B = μ n I B = μ n I | https://openstax.org/books/university-physics-volume-2/pages/12-key-equations |
Ampèreâs law : physical law that states that the line integral of the magnetic field around an electric current is proportional to the current | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
Biot-Savart law : an equation giving the magnetic field at a point produced by a current-carrying wire | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
diamagnetic materials : their magnetic dipoles align oppositely to an applied magnetic field; when the field is removed, the material is unmagnetized | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
ferromagnetic materials : contain groups of dipoles, called domains, that align with the applied magnetic field; when this field is removed, the material is still magnetized | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
hysteresis : property of ferromagnets that is seen when a materialâs magnetic field is examined versus the applied magnetic field; a loop is created resulting from sweeping the applied field forward and reverse | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
magnetic domains : groups of magnetic dipoles that are all aligned in the same direction and are coupled together quantum mechanically | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
magnetic susceptibility : ratio of the magnetic field in the material over the applied field at that time; positive susceptibilities are either paramagnetic or ferromagnetic (aligned with the field) and negative susceptibilities are diamagnetic (aligned oppositely with the field) | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
paramagnetic materials : their magnetic dipoles align partially in the same direction as the applied magnetic field; when this field is removed, the material is unmagnetized | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
permeability of free space : μ0,μ0,measure of the ability of a material, in this case free space, to support a magnetic field | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
solenoid : thin wire wound into a coil that produces a magnetic field when an electric current is passed through it | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
toroid : donut-shaped coil closely wound around that is one continuous wire | https://openstax.org/books/university-physics-volume-2/pages/12-key-terms |
The magnetic field created by a current-carrying wire is found by the Biot-Savart law. | https://openstax.org/books/university-physics-volume-2/pages/12-summary |
The current elementIdlâIdlâproduces a magnetic field a distanceraway. | https://openstax.org/books/university-physics-volume-2/pages/12-summary |
The strength of the magnetic field created by current in a long straight wire is given byB=μ0I2ÏRB=μ0I2ÏR(long straight wire) whereIis the current,Ris the shortest distance to the wire, and the constantμ0=4ÏÃ10â7Tâm/sμ0=4ÏÃ10â7Tâm/sis the permeability of free space. | https://openstax.org/books/university-physics-volume-2/pages/12-summary |
The direction of the magnetic field created by a long straight wire is given by right-hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of current, and the fingers curl in the direction of the magnetic field loops created by it. | https://openstax.org/books/university-physics-volume-2/pages/12-summary |
The force between two parallel currentsI1I1andI2,I2,separated by a distancer, has a magnitude per unit length given byFl=μ0I1I22Ïr.Fl=μ0I1I22Ïr. | https://openstax.org/books/university-physics-volume-2/pages/12-summary |
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