A 279-turn solenoid with a length of 32 cm and radius of 2.2 cm carries a curren

Question

A 279-turn solenoid with a length of 32 cm
and radius of 2.2 cm carries a current of 2 A. A
second coil of 4 turns is wrapped tightly about
this solenoid so that it can be considered to
have the same radius as the solenoid.
A)Find the change in the magnetic flux
through the coil when the current in the
solenoid increases to 5.2 A in a period of
0.77 s. The permeability of a vacuum is
4 × 10^7 T · m/A
Answer in units of T · m^2.

BFind the magnitude of the average induced
emf in the coil.
Answer in units of V.

Explanation / Answer

(a) n = 279 / 0.22 = 1268 µo = 4 p x 10^-7 T. m / A I = 5.2 amps - 2.0 amps r = 2.2 cm = 0.022 m A = p r^2 from the theory we have the equation B = µo n I ? = 0o so the change in magnetic flux will be ?FB = B A cos? =.............. T . m2 (b) N = 4 ?t = 0.77 s the magnitude of the average induced emf in the coil will be e = N ?FB /?t = ……. V

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