Calculate emf The magnitude of the magnetic field encircled by a single loop of

Question

Calculate emf The magnitude of the magnetic field encircled by a single loop of wire, 10 cm in radius and of 7.4 resistance, changes with time as shown in Fig. 31-30. Calculate the magnitude of the emf in the loop as a function of time for each of the following time intervals. The (uniform) magnetic field is perpendicular to the plane of the loop.

Figure 31-30
(a) t = 0 to t = 2.0 s
V
(b) t = 2.0 s to t = 4.0 s
V
(c) t = 4.0 s to t = 6.0 s
V

Section 31.4 Faraday's Law

DIAGRAM

http://img838.imageshack.us/i/3142.gif/

Explanation / Answer

(a )

emf = - d / dt ,

e = - A . dB / dt

A = ( 0.1^2 ) = 0.0314159 m^2 ;

for t= 0 to t = 2 ,

dB / dt = 0.5 / 2 = 0.25 T /s ;

e = - 0.0314159 * 0.25 = - 7.85 e -3 V , <-----------ans

( b )

e = - 0.0314159 * 0 ; [ since dB / dt = 0 , B doesnt change , ]

or e = 0 ; <-------ans

( c )

fot t= 4 to t= 6 ,

dB /dt = 0-0.5 / ( 6 -4 ) = -0.25 ;

e = - 0.0314159 * -0.25 = + 7.85 e -3 V <--------ans

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