Hermione has a gold ring that is 4.50 cm in diameter, and she places it between

Question

Hermione has a gold ring that is 4.50 cm in diameter, and she places it between the poles of a large electromagnet, with its area vector pointing parallel to the magnetic field direction created by the electromagnet. The initial uniform field of 3.0 T decreases steadily at 0.230 T/s. She needs to create an E field in the ring (since amazingly this wards off the evil Dementors); what is the magnitude of the E field induced in the ring ? There is also an induced current in the gold ring. Which direction (clockwise or counterclockwise) is the induced current, seen by Myrtle Elizabeth Warren who is located on the magnet's S pole? (I don't know why Myrtle is at the S pole of a magnet, no wonder she is moaning in this particular case!) Counterclockwise Clockwise

Explanation / Answer

given

d = 4.5 cm

r = d/2 = 4.5/2 = 4.5/2 = 2.25 cm = 0.0225 m

dB/dt = 0.23 T/s

A) induced emf in the ring, V = A*dB/dt

= pi*r^2*dB/dt

= pi*0.0225^2*0.23

= 3.66*10^-4 volts

so, E = V/(2*pi*r)

= 3.66*10^-4/(2*pi*0.0225)

= 2.6*10^-3 V/m

B) Counterclockwise (According to Lenz's law)

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