A flat, circular, steel loop of radius 30 cm is at rest in a uniform magnetic fi

Question

A flat, circular, steel loop of radius 30 cm is at rest in a uniform magnetic field, as shown in an edge on view in the figure below. The field is changing with time, according to

1 10 A flat, circular, steel loop of radius 30 cm is at rest in a uniform magnetic field, as shown in an edge on view in the figure below. The field is changing with time, according to B(t) = (1.4 T)e?(0.089 s-1)t.. Find the emf induced in the loop as a function of time. When is the induced emf equal to of its initial value? Find the direction of the current induced in the loop, as viewed from above the loop. clockwise counterclockwise

Explanation / Answer

a)

A=pir^2 =pi*0.3^2=0.2827 m^2

dB/dt =-0.089*1.4 e^-(0.089t)

dB/dt =-0.1246e^-(0.089t)

E=-Asin60(dB/dt)

E=-0.2827*sin60*[-0.1246e^-(0.089t)]

E=0.0305 e^(-0.089t)

b)

E=Eo/10

0.0305 e^(-0.089t) =0.0305/10

t=25.9 s

c)counter clockwise

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