30. Induction and Inductance

What emf is created in a $1.3\mathrm{m}$ long conductor moving at $45\text{m/s}$ in a $3.0\text{mT}$ magnetic field? Assume the conductor's velocity is perpendicular to the field.

If the metal triangle shown in the figure is pushed to the left, farther into the magnetic field, what is the direction of the induced current in the triangle?

In a region of space, a magnetic field is increasing at $3\mathrm{T}/\mathrm{s}$. A square loop of wire with a side of $12\mathrm{cm}$ is oriented perpendicular to the field. The loop has a total resistance of $0.02\mathrm{\Omega }$. What current is induced in the loop?

A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of dB/dt = -0.680 T/s.

(a) Is the induced current in the loop clockwise or counterclockwise?

The current in Fig. E29.18 obeys the equation I(t) = I_0e^(-bt), where b > 0.

Find the direction (clockwise or counterclockwise) of the current induced in the round coil for t > 0.

A circular loop of wire is in a region of spatially uniform mag-netic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure.

Determine the direction (clockwise or counterclock-wise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value B_0. Explain your reasoning.

Using Lenz's law, determine the direction of the current in resistor ab of Fig. E29.19 when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.

A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. E29.20. Terminals a and bof winding A may be connected to a battery through a revers-ing switch. State whether the induced current in the resistor Ris from left to right or from right to left in the following circumstances: (a) the current in winding Ais from a to b and is increasing; (b) the current in winding A is from b to a and is decreasing; (c) the current in winding A is from b to a and is increasing.

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. (b) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

A single loop of wire with an area of 0.0900 m^2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (b) If the loop has a resistance of 0.600 Ω, find the current induced in the loop.