A circular coil enclosing an area of 95 . 3 cm 2 is made of 270 turns of copper

Question

A circular coil enclosing an area of 95.3 cm2 is made of 270 turns of copper wire as shown in the figure. When viewed from the right the coil is wound counter-clockwise. A 6.3 ? re- sistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 3.04 T points horizontally from left-to-right through the perpendicular plane of the coil.

During a 4.7 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

A circular coil enclosing an area of 95.3 cm2 is made of 270 turns of copper wire as shown in the figure. When viewed from the right the coil is wound counter-clockwise. A 6.3 ohm resistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 3.04 T points horizontally from left-to-right through the perpendicular plane of the coil. During a 4.7 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

The induce emf = N*d?/dt = N*A*dB/dt Now the value of dB/dt = (3.04- (-3.04))/(4.7min*60s/min) =

= 2.15x10^-2T/s

So emf = 270*95.3x10^-4m^2*2.15x10^-2 = 55.321x10^-3V

Now i = V/R = 55.321x10^-3V/6.3? = 8.78x10^-3A

Since i = dq/dt then the charge Q = i*t = 8.78x10^-3*(4.7min*60) = 2.476C

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