A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B = Bmax et, where Bmax and rare constants. The field has the constant value Bmax for t < 0. Find the emf induced in the loop as a function of time. (Use the following as necessary: A, Bmax t, and r.) 8=

A solenoid with 4 x 107turns/m has an iron core placed in it whose magnetic susceptibility is 4.0 x 103. (a) If a cent of 2.0 A flows through the solenoid, what is the magnetic field in the iron core? (b) What is the effective surface current formed by the aligned atomic current loops in the iron core? (c) What is the self-inductance of the filled solenoid?

A single-turn circular loop of wire of radius 50 mm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.10-s time interval, the magnitude of the field Increases uniformly from 200 to 300 mT. (a) Determine the emf Induced in the ioop. (b) If the magnetic field is directed out of the page, what is the direction of the cun-ent induced in the loop?

The conducting rod shown in the accompanying figure moves along parallel metal rails that are 25-cm apart. The system is in a uniform magnetic field of strength 0.75 T, which is directed into the page. The resistances of the rod and the rails are negligible, but the section PQ has a resistance of 0.25 . (a) What is the emf (including its sense) induced in the rod when it is moving to tire right with a speed of 5.0 m/s? (b) What force is required to keep the rod moving at this speed? (c) What is the rate at which work is done by this force? (d) What is the power dissipated in the resistor?

A 5000-pF capacitor is charged to 100 V and then quickly connected to an 80-mH inductor. Determine (a) the maximum energy stored in the magnetic field of the inductor, (b) the peak value of the current, and (c) the frequency of oscillation of the circuit.

The flip coil of the preceding problem has a radius of 3.0 cm and is wound with 40 turns of copper wire. The total resistance of tire coil and ballistic galvanometer is 0.20 When the coil is flipped through 180° in a magnetic fielda change of 0.090 C flows through the ballistic galvanometer. (a) Assuming that and the face of the coil are initially perpendicular, what is tire magnetic field? (b) If the coil is flipped through 90°, what is tire reading of the galvanometer?

The normal to tt plane of a single-turn conducting loop is directed at an angle to a spatially uniform magnetic field B. It has a fixed area and orientation relative to the magnetic fleck Show that the emf induced In the loop is given by i = (dB/dt)(Acos),where A is the area of the loop.

Check Your Understanding (a) What is the magnetic flux through one turn of a solenoid of self- inductance 8.0 × 10-5 H when a current of 3.0 A flows through it? Assume that the solenoid has 1000 turns and is wound from wire of diameter 1.0 mm. (b) What is the cross-sectional area of the solenoid?

Suppose that a rectangular toroid has 2000 windings and a self-inductance of 0.040 H. If h = 0.10 m, what is the current flowing through a rectangular toroid when the energy in its magnetic field is 2.0 × 10-6 J?

What is the self-inductance per meter of a coaxial cable whose inner radius is 0.50 mm and whose outer radius is 4.00 mm?