Q1 A 170-turn coil of radius 3.1 cm and resistance 7.8 is coaxial with a solenoi

Question

Q1 A 170-turn coil of radius 3.1 cm and resistance 7.8 is coaxial with a solenoid of 180 turns/cm and diameter 4.2 cm. The solenoid current drops from 1.2 A to zero in time interval t = 29 ms. What current is induced in amperes in the coil during t?

Q2 An electric generator contains a coil of 100 turns of wire, each forming a rectangular loop 39.6 cm by 41.8 cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 3.88 T and initially perpendicular to the coil's plane. What is in volts the maximum value of the emf produced when the loop is spun at 1430 rev/min about an axis perpendicular to the magnetic field?

Q3 A long solenoid has a diameter of 15.1 cm. When a current i exists in its windings, a uniform magnetic field of magnitude B = 27.5 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 9.03 mT/s. Calculate the magnitude of the induced electric field (a) 4.03 cm and (b) 10.9 cm from the axis of the solenoid.

Need help please and thaank you!!

Explanation / Answer

1) B = mu0 n I

E = N * dphiB/dt

dphiB/dt = A * dB/dt = A * mu0 n * dI/dt

dI/dt = 1.2 / 29 * 10-3 = 41.38 A/s

A = pi * 0.0212 = 1.38 * 10-3 m2

dphiB/dt = 1.38 * 10-3 * 4 pi * 10-7 * 18000 * 41.38 = 1.29 * 10-3

E = 170 * 1.29 * 10-3 = 0.219 V

I' = E / R = 0.219 / 7.8

= 0.028 A

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