Question

A small circular loop of area 2.20 cm2 is placed in the plane of, and concentric with, a large circular loop of radius 1.23 m. The current in the large loop is changed at a constant rate from 219 A to -219 A (a change in direction) in a time of 1.14 s, starting at t = 0.What is the magnitude of the magnetic field at the center of the small loop due to the current in the large loop at (a) t = 0, (b) t = 0.570 s, and (c) t = 1.14 s? (d) From t = 0 to t = 1.14 s, is B reversed? Because the inner loop is small, assume is uniform over its area. (e) What emf is induced in the small loop at t = 0.570 s?

Answer #1

**given**

**dI/dt = (-219-219)/1.14 = -384.2**

**dI = -384.2*dt**

**I = integral dI**

**I = Io - 384.2*t**

**Io = 219 A**

**I = 219 - 384.2*t**

**magnetic field B due to large loop B =
uo*I/(2R)**

**part(a)**

**at t = 0**

**I = 219**

**B = 4*pi*10^-7*219/(2*1.23)**

**B = 1.1*10^-4 T**

**part(b)**

**at t = 0.57 s**

**I = 219 - (384.2*0.57) = 0.006 A**

**B = 4*pi*10^-7*0/(2*1.23)**

**B = 0**

**part(c)**

**at t = 1.14 s**

**I = 219 - 384.2*1.14 = -219 A**

**B = -4*pi*10^-7*219/(2*1.23)**

**B = -1.1*10^-4 T**

**B is reversed**

**part(d)**

**flux = B*A = uo*I*A/(2R) = ( A*uo/2R)*(Io -
384.2*t)**

**EMF = -(d/dt)*flux**

**EMF = ( A*uo/2R)*384.2**

**emf = 2.2*10^-4*4pi*10^-7*384.2/(2*1.23)**

**emf = 4.32*10^-8 T**

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