Problem 1: A closed loop of wire of radius R = 0.45 m is in the presence of a un

Question

Problem 1: A closed loop of wire of radius R = 0.45 m is in the presence of a uniform magnetic field as shown in the figure. The magnitude of the magnetic field is changing according to the following equation: B=B0(1 + e-kr) The variables k and Bo in this equation are 0.35 s1 and 6.5 mT, respectively. Part (a) What is the magnitude of the induced electric field (in V/m) at t-25? Numeric : A numeric value is expected and not an expression. E= Part (b) What is its direction (clockwise or counterclockwise)? MultipleChoice: 1) Clockwise

Explanation / Answer

Induced electric field E = (R/2) (dB/dt)
B = Bo( 1+ e-kt )
dB / dt = - Bok e-kt
at t=2 sec, dB/dt = - 6.5x10-3 e- 0.35*2 = -3.22x10-3
at t=2 sec, E = -0.45 * 3.22x10-3 / 2 = -7.26x10-4 V/m
magnitude of E = 726 micro V/m

As dB/dt is -ve, dircetion of electric filed is clockwise, so that induced current in the loop opposes the decreasing magnetic flux through the loop.

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