A circular coil enclosing an area of 138 cm^2 is made of 130 turns of copper wir

Question

A circular coil enclosing an area of 138 cm^2 is made of 130 turns of copper wire as shown in the figure. When viewed from the right the coil is wound counter-clockwise. A 9.2 Ohm resistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 2.3 T points horizontally from left-to-right through the perpendicular plane of the coil. During a 2 minute time interval the field uniformly changes at a constant rate, until a reversed field is reached equal in magnitude to the initial field. How much charge flows through the coil? Answer in units of C.

Explanation / Answer

An emf will be induced in the coil due to change in flux. The magnitude of emf will be:

e = - N d(phi)/dt = N A (B1 - B2)/t

N = 130 ; A = 138 cm^2 = 0.0138 m^2 ; B1 = 2.3 and B2 = -2.3 ; t = 2 min = 120 sec

e = 130 x 0.0138 (2.3 - (-2.3)/120 = 0.0688 Volts

From Ohm's law, V = IR => I = V/R = e/R

I = 0.0688/9.2 = 0.0075 A

we know that, I = Q/t

Q = I x t = 0.0075 x 120 = 0.9 C

Hence, Q = 0.9 C.

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