The figure below shows a conducting loop consisting of half-circle of radius r a

Question

The figure below shows a conducting loop consisting of half-circle of radius r and three straight sections. The half-circle lies in a uniform magnetic field B that is directed out of the page; the magnetic field is given by B = 4.0t2 + 2.0t + 3.0, with B in tesla and t in seconds. An ideal battery with emf ebat = 2.0 V is connected to the loop. If the radius is 0.20 m and the resistance if 2.0 ohm (a) what is the magnitude and direction of the induced emf rhoind around the loop by the magnetic field B at t = 10 s? (b) What is the current in the loop at t = 10 s?

Explanation / Answer

A)
dB/dt = 8*t + 2

at t = 10 s

dB/dt = 8*10+2

= 82 T/s

A = pi*r^2/2
= pi*0.2^2/2
= 0.0628 m^2

we induced emf = A*dB/dt

b) i = (induced emf - Ebat)/R

= (5.15 - 2)/2

= 1.575 A

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