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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(-tτ), whereB0andτare 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

B0πr2τe-tτ

Step by step solution

01

Given

B=B0e-tτ

02

Understanding the concept

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

Formula:

ε=-Ndϕdt

ϕ=BA

03

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

We have,

ε=-dϕdt

We also have,

ϕ=BA

Here,

As the cross-section is circular,

A=πr2

ϕ=Bπr2

We also have,

B=B0e-tτϕ=B0e-tτπr2ε=-dB0e-tτπr2dtε=B0πr2e-tτ-tτε=B0πr2eτe-tτ

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Most popular questions from this chapter

In Figure, ε=100V,R1=10.0Ω,R2=20.0Ω,R3=30.0Ω,andL=2.00H.Immediately after switch S is closed, (a) what is i1? (b) what is i2? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative values.) A long time later, (c) what is i1? (d) what is i2? The switch is then reopened. Just then, (e) what is i1? (f) what is i2? A long time later, (g) what is i1? (h) what is i2?

Two coils connected as shown in Figure separately have inductances L1 and L2. Their mutual inductance is M. (a) Show that this combination can be replaced by a single coil of equivalent inductance given by

Leq=L1+L2+2M

(b) How could the coils in Figure be reconnected to yield an equivalent inductance of

Leq=L1+L2-2M

(This problem is an extension of Problem 47, but the requirement that the coils be far apart has been removed.)

Figure 30-30 gives the variation with time of the potential difference VRacross a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance Rand emf εbut differ in the inductance L . Rank the circuits according to the value of L, greatest first.

Figure 30-27 shows a circuit with two identical resistors and an ideal inductor.

Is the current through the central resistor more than, less than, or the same as that through the other resistor (a) just after the closing of switch S, (b) a long time

after that, (c) just after S is reopened a long time later, and (d) a long time after that?

In Figure (a), the inductor has 25 turns and the ideal battery has an emf of 16 V. Figure (b) gives the magnetic fluxφ through each turn versus the current i through the inductor. The vertical axis scale is set by φs=4.0×10-4Tm2, and the horizontal axis scale is set by is=2.00AIf switch S is closed at time t = 0, at what ratedidtwill the current be changing att=1.5τL?
See all solutions

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