Question

A coil 5.00 cm in radius, containing 250 turns, is
placed in a uniform magnetic field that varies with time according
to:

B = (0.230 T/s)t + (4.00 x 10^{-5}
T/s^{5})t^{5}. The coil is connected to
a 450 ohm resistor, and its plane is perpendicular to the magnetic
field. The resistance of the coil can be
neglected. Find the induced emf in the coil as a
function of time.

Answer #1

Induced EMF is given by:

EMF = -N*d(phi)/dt

phi = Magnetic flux = B*A*cos theta

So, EMF = -N*A*cos theta*dB/dt

N = number of turns = 250.0 turns

A = area = pi*0.05^2 = 7.85*10^-3 m^2

B = magnetic field = (0.230 T/s)t + (4.00 x 10^{-5}
T/s^{5})t^{5}

then, dB/dt = (0.230 T/s)*1 + (5*4.00 x 10^{-5}
T/s^{5})t^{5-1}

dB/dt = (0.230) + (2.00 x 10^{-4})t^{4}

since, plane of coil is perpendicular to the magnetic field

So, theta = 0 deg, cos theta = 1

then, EMF = -250*7.85*10^-3*cos 0 deg*[(0.230) + (2.00 x
10^{-4})t^{4}]

**EMF = -0.451375 - 3.925*10^-4*t^4**

**EMF = -(0.451375 -
3.925*10 ^{-4}*t^{4})**

"Let me know if you have any query."

#5. A coil 5.00 cm in radius, containing 250
turns, is placed in a uniform magnetic field that varies with time
according to:
B = (0.230 T/s)t + (4.00 x 10-5
T/s5)t5. The coil is connected to
a 450 ohm resistor, and its plane is perpendicular to the magnetic
field. The resistance of the coil can be
neglected. Find the induced emf in the coil as a
function of time. (20 pts.)

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