A circular coil in the plane of the paper lies in a 0.75T magnetic field pointin

Question

A circular coil in the plane of the paper lies in a 0.75T magnetic field pointing into the paper. If the loop's diameter changes from 20.0 cm to 6.0cm in 0.50s, what is the direction and magnitude of the average induced emf, and if the coil's resistance is 2.5ohm what is the average induced current? A circular wire loop of radius r = 1 2cm is immersed in a uniform magnetic field of B= 0.500T with its plane normal to the direction of the field. If the field magnitude then decreases at a constant rate of -0.010T/s, at what rate should r increase so that induced emf within the loop is zero?

Explanation / Answer

9)

Part A : = BACos

Change 20 cm and 6 cm into 0.2 m and 0.06 m.

Divide them both by 2 to find the radius. Now we have 0.1 and 0.03 m.

Now use = (*0.1^2)(0.75 T)cos0

= 0.023562 Wb.

Now use the other radius, = (*o.03^2)(.75 T)cos0

= 0.0021206 Wb.

Now use =-N(/t)

= (0.023562-0.0021206)/.5

= 43 mV clockwise

part B.

To find the current, use I=/R

I = 0.04288 / 2.5 = 0.017152 = 0.017 A

10)

according to Faraday's law, electric motion force is:

E = - N (d/dt) = -N d(BA)/dt = -NA dB/dt - NB dA/dt

E = -NA dB/dt - NB d(r²)/dt = -NA dB/dt - NB 2r(dr/dt)

N = 1
r = 0.12 meter
B = 0.5 T
dB/dt = - 0.010 T/s


E = -A dB/dt - 2rB (dr/dt)

0 = -(r²) dB/dt - 2rB (dr/dt)

0 = -( * 0.12²) (–0.010) - 2(0.12)(0.5) (dr/dt)

dr/dt = 1.2*10^-3 m/s

dr/dt = 1.2 m m/s

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