Chapter 30: Electromagnetic Induction

A $2.0cm\times 2.0cm$square loop of wire with resistance$0.010\Omega$has one edge parallel to a long straight wire. The near edge of the loop is cm from the wire. The current in the wire is increasing at the rate of $100A/s$. What is the current in the loop?

FIGURE shows a $4.0$-cm-diameter loop with resistance $0.10\Omega$around a $2.0$-cm-diameter solenoid. The solenoid is $10$ cm long, has $100$turns, and carries the current shown in the graph. A positive current is $cw$when seen from the left. Find the current in the loop at$\left(a\right)t=0.5s,\left(b\right)t=1.5s,and\left(c\right)t=2.5s.$

FIGURE P30.47 shows a 1.0-cm-diameter loop with $R=0.50\mathrm{\Omega }$inside a 2.0-cm-diameter solenoid. The solenoid is 8.0cm long, has 120 turns, and carries the current shown in the graph. A positive current is $\text{CW}$when seen from the left. Determine the current in the loop at$t=0.010\mathrm{s}$

FIGURE$\mathrm{P}30.48$shows two $20$-turn coils tightly wrapped on the same$2.0-\mathrm{cm}$-diameter cylinder with $1.0-\mathrm{mm}$-diameter wire. The current through coil $1$is shown in the graph. Determine the current in coil $2$at (a) $\mathrm{t}=0.05\mathrm{s}$and (b) . A positive current is $\mathrm{t}=0.25\mathrm{s}$into the page at the top of a loop. Assume that the magnetic field of coil localid="1648920663723" $1$passes entirely through coil localid="1648920667724" $2$.

An electric generator has an 18 -cm-diameter, 120 -turn coil that rotates at 60 $\mathrm{Hz}$in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to generate a peak voltage of 170$\mathrm{V}$?

The two loops of wire in FIGURE are stacked one above the other. Does the upper loop have a clockwise current, a counterclockwise current, or no current at the following times? Explain. a. Before the switch is closed.

b. Immediately after the switch is closed.

c. Long after the switch is closed.

d. Immediately after the switch is reopened.

FIGURE EX30.5 shows a $10\mathrm{cm}\times 10\mathrm{cm}$square bent at a ${90}^{\circ }$angle. A uniform $0.050\mathrm{T}$magnetic field points downward at a ${45}^{\circ }$angle. What is the magnetic flux through the loop?

A 40-turn, 4.0-cm-diameter coil with $R=0.40\mathrm{\Omega }$ surrounds a 3.0-cm-diameter solenoid. The solenoid is 20 cm long and has 200 turns. The

60 $\mathrm{Hz}$current through the solenoid is I = $I_0\sin \left(2\pi ft\right)$. What is $I_0$ if the maximum induced current in the coil is $0.20\mathrm{A}?$?

A small, 2.0-mm-diameter circular loop with $R=0.020\Omega$is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from $+1.0A$to $-1.0A$in $0.10s$. What is the induced current in the inner loop?

A rectangular metal loop with $0.050$ resistance is placed next to one wire of the RC circuit shown in $FIGUREP30.52$. The capacitor is charged to $2V$with the polarity shown, then the switch is closed at $t=0s$.

a. What is the direction of current in the loop for $t>0s$?

b. What is the current in the loop at $t=5.0\mu s$? Assume that

only the circuit wire next to the loop is close enough to produce a significant magnetic field.