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Chapter 30: Q82P (page 901)

A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according toB=B0e(-t蟿), whereB0and蟿are constants. Find an expression for the emf in the loop as a function of time.

Short Answer

Expert verified

Equation for the emf in the loop as a function of time will be

B0蟺r2蟿e-t蟿

Step by step solution

01

Given

B=B0e-t蟿

02

Understanding the concept

We use Lenz鈥檚 law for induced emf, we rearrange the formula to get the equation for the emf in the loop as a function of time.

Formula:

蔚=-Nd蠒dt

蠒=BA

03

Calculate the Equation for the emf in the loop as a function of time

We have,

蔚=-d蠒dt

We also have,

蠒=BA

Here,

As the cross-section is circular,

A=蟺r2

蠒=B蟺r2

We also have,

B=B0e-t蟿蠒=B0e-t蟿蟺r2蔚=-dB0e-t蟿蟺r2dt蔚=B0蟺r2e-t蟿-t蟿蔚=B0蟺r2e蟿e-t蟿

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Most popular questions from this chapter

The magnetic field of a cylindrical magnet that has a pole-face diameter of 3.3 cmcan be varied sinusoidally between 29.6 Tand 30.0 Tat a frequency of 15Hz. (The current in a wire wrapped around a permanent magnet is varied to give this variation in the net field.) At a radial distance of 1.6 cm, what is the amplitude of the electric field induced by the variation?

In Figure, the magnetic flux through the loop increases according to the relation 蠁B=6.0t2+7.0t, where蠁Bis in milli-Weber and t is in seconds. (a) What is the magnitude of the emf induced in the loop when t = 2.0 s? (b) Is the direction of the current through R to the right or left?

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Figure shows a rod of length L = 10.0 cm that is forced to move at constant speed v = 5.0 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400惟; the rest of the loop has negligible resistance. A current i = 100 Athrough the long straight wire at distance a = 10.0 mm from the loop sets up a (non-uniform) magnetic field through the loop. (a) Find the emf. (b) Find the current induced in the loop. c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed?(e) At what rate does this force do work on the rod?

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