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blsea [12.9K]
3 years ago
10

The current in a long solenoid of radius 4 cm and 19 turns/cm is varied with time at a rate of 8 A/s. A circular loop of wire of

radius 6 cm and resistance 3 Ω surrounds the solenoid. Find the electrical current induced in the loop (in µA).
Physics
1 answer:
Dmitry [639]3 years ago
4 0

Answer:

Current induced in the loop = 0.032 mA

Explanation:

emf induced in the solenoid using Faraday law e = \frac{-d\phi}{dt}=-\pi R^{2} \frac{dB}{dt}

here, R is the radius of solenoid which is constant &  \frac{dB}{dt} is the change in magnetic field.

Magnetic field inside the solenoid from B=μ0 n i -----(i)

Where, i is the current in the coil.

n= numbers of turn in per meter length.

n=19 x 100 turns/m

Differentiating equation (i)

\frac{dB}{dt} = μ0 n \frac{dI}{dt}

= 4 π 10-7 x 1900 x 8 =0.019

E = 3.14 X 0.42^{2}  X 0.019 =0.095 m V

Hence electrical current induced in the loop =  \frac{E}{R} =\frac{0.095}{3} = 0.032 mA

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