Q: A rectangular loop of area $A$ rotates with angular velocity $\omega$ in a uniform magnetic field $B$ (seventeenth image). What is the maximum induced emf?

$\mathcal{E}_{\text{max}} = \omega B A$

Question 1

An electron is projected with an initial velocity $v_0$ perpendicular to a uniform magnetic field and follows a semicircular path from point A to point B, as shown in the first image. If the radius of the path is $R = 0.05\ \mathrm{m}$ and $v_0 = 1.60 	imes 10^6\ \mathrm{m/s}$, what is the magnitude of the magnetic field $B$ required for this motion?

Accepted Answer

$B = \frac{mv_0}{qR}$

Question 2

In the Hall effect setup shown in the second image, a silver ribbon carries a current $I$ in the $+x$ direction and is placed in a uniform magnetic field $\vec{B}$ in the $+y$ direction. If the ribbon has width $z_1$ and thickness $y_1$, and the number density of free electrons is $n$, what is the expression for the Hall electric field $E$ in the $z$-direction?

Accepted Answer

$E = \frac{IB}{ne y_1 z_1}$

Question 3

A voice coil in a loudspeaker (third image) has $N$ turns, diameter $d$, and carries current $I$ in a magnetic field $B$ at an angle $60^\circ$ from the normal to the coil. What is the magnitude of the net magnetic force on the coil?

Accepted Answer

$F = \pi N I B d \cos(30^\circ)$

Question 4

A square loop of side $L$ (fourth image) carries a current $I$ in the clockwise direction and is placed in a non-uniform magnetic field $\vec{B} = \frac{B_0 z}{L} \hat{j} + \frac{B_0 y}{L} \hat{k}$. What is the magnitude of the net force on the loop?

Accepted Answer

$F_{	ext{net}} = I L B_0$

Question 5

Two short wire segments, each of length $2.00\ \mathrm{mm}$, carry a current $I = 26.0\ \mathrm{A}$ and are arranged at a right angle as shown in the fifth image. What is the direction of the magnetic field at point $P$, midway between the segments?

Accepted Answer

Into the page

Question 6

In the sixth image, wire $CD$ is free to slide vertically above wire $AB$. Both wires carry current $I$ in opposite directions. If the mass per unit length of $CD$ is $\lambda$, what is the equilibrium height $h$ where $CD$ will float due to the magnetic force?

Accepted Answer

$h = \frac{\mu_0 I^2}{2 \pi \lambda g}$

Question 7

A square loop of side $a$ is placed a distance $d$ from an infinite straight wire carrying current $I_2$ (seventh image). The loop carries current $I_1$. What is the net force on the loop in terms of $a$, $d$, $I_1$, and $I_2$?

Accepted Answer

$F = \frac{\mu_0 a^2 I_1 I_2}{2 \pi (d^2 - a^2/4)}$

Question 8

A coaxial cable consists of an inner conductor of radius $a$ and an outer conductor of radius $b$ (eighth image). Both carry equal and opposite currents $I$. What is the self-inductance per unit length $\mathcal{L}/l$ of the cable?

Accepted Answer

$\mathcal{L}/l = \frac{\mu_0}{2\pi} \ln\left(\frac{b}{a}\right)$

Question 9

A spherical shell of radius $R$ and total charge $Q$ rotates about the $z$-axis with angular speed $\omega$ (ninth image). What is the total magnetic moment $\mu$ of the shell?

Accepted Answer

$\mu = \frac{Q \omega R^2}{3}$

Question 10

A rectangular loop of width $b$ and length $L$ is pulled to the right at constant speed $v$ near a long straight wire carrying current $I$ (tenth image). What is the magnitude of the induced emf in the loop?

Accepted Answer

$\mathcal{E} = \frac{\mu_0 I b v}{2\pi r(r+a)}$

Question 11

In the electromagnetic induction experiment (eleventh image), when the switch $S$ is opened after being closed for several minutes, what is the direction of the induced current in resistor $ab$?

Accepted Answer

From $a$ to $b$

Question 12

A metal bar of length $L$ slides down frictionless rails inclined at angle $\phi$ in a uniform magnetic field $B$ (twelfth image). What is the terminal speed $v_T$ of the bar?

Accepted Answer

$v_T = \frac{mgR \sin\phi}{(B L \cos\phi)^2}$

Question 13

The graph (thirteenth image) shows the current $i$ versus time $t$ for an RLC circuit. What type of damping does this circuit exhibit?

Accepted Answer

Underdamped

Question 14

A square loop moves with velocity $\vec{v}$ away from a long straight wire carrying current $I$ (fourteenth image). What is the direction of the induced current in the loop as it moves away?

Accepted Answer

Clockwise

Question 15

A rectangular loop of wire is placed in a uniform magnetic field $\vec{B}$ directed out of the page (fifteenth image). If the magnitude of $B$ decreases steadily, what is the direction of the induced current in the loop?

Accepted Answer

Counterclockwise

Question 16

A circular loop of radius $r$ is placed in a uniform magnetic field $\vec{B}$ directed out of the page (sixteenth image). If the field is increasing, what is the direction of the induced current?

Accepted Answer

Clockwise

Question 17

A rectangular loop of area $A$ rotates with angular velocity $\omega$ in a uniform magnetic field $B$ (seventeenth image). What is the maximum induced emf?

Accepted Answer

$\mathcal{E}_{	ext{max}} = \omega B A$

Question 18

A coaxial cable (eighteenth image) carries current $I$ in opposite directions in the inner and outer conductors. What is the magnetic field at a distance $r$ such that $a < r < b$?

Accepted Answer

$B = \frac{\mu_0 I}{2\pi r}$

Question 19

In the RL circuit (nineteenth image), just after switch $S_1$ is closed, what is the potential difference $V_{ab}$ across the resistor $R$?

Accepted Answer

$V_{ab} = 0$

Question 20

In the circuit with an inductor and multiple resistors (twentieth image), just after the switch is closed, what is the current through the inductor?

Accepted Answer

Zero

Question 21

In the RLC circuit (twenty-first image), what is the condition for critical damping?

Accepted Answer

$R = 2\sqrt{\frac{L}{C}}$

Question 22

In the LC circuit (twenty-second image), what is the maximum charge $Q_{max}$ the capacitor will receive if the initial current in the inductor is $I_{max}$?

Accepted Answer

$Q_{max} = I_{max} \sqrt{LC}$

Question 23

In the circuit with two inductors and multiple resistors (twenty-third image), just after the switch is closed, which ammeters will read a nonzero current?

Accepted Answer

Only $A_1$ and $A_4$

Question 24

In the circuit with two resistors and an inductor (twenty-fourth image), long after the switch is closed, what is the current through $R_2$?

Accepted Answer

Zero

Physics 1C: Magnetic Forces, Induction, and Circuits – Visual Study Guide

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