A circular coil enclosing an area of 85.6 em2 is made of 260 turns of copper wir

Question

A circular coil enclosing an area of 85.6 em2 is made of 260 turns of copper wire as shown in the figure. When viewed from the right the coil is wound counter-clockwise. An 8.4 re- sistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 2.88 T points horizontally from left-to-right through the perpendicular plane of the coil. Magnetic Field B(t) During a 6.5 minute time interval the field uniformly changes at a constant rate, until a reversed field is reached equal n magnitude to the initial field. How much charge flows through the coil? Answer in units of C

Explanation / Answer

Given

circular coil of area A = 85.6*10^-4 m2, with no of turns n = 260

R = 8.4 ohm

B1 = 2.88 T

final magnetic field is B2 = -2.88 T

dt = 6.5 minutes = 6.5*60 = 390 s

From Faraday's law e = -dphi/dt

by definition of magnetic flux phi = B*A cos theta here theta is zero

e = -(phi2-phi1)/dt

I*R = -n*A(B2-B1)/dt

(q/t)(R)= -n*A(B2-B1)/dt

q = (-n*A(B2-B1)/dt)(t/R)

q = -n*A(B2-B1)*/R

q = -260(-2.88-2.88)/8.4 = 178 C

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