A long solenoid with 15 turns per cm has a small loop of area 2 cubic cm placed inside the solenoid to its axis. If the current carried by the solenoid changes steadily from 2 Ampere to 4 Ampere in 0.1 second. What is the induced emf in the loop while the current is changing.

Science

Class 12

987

Aanya

Alexandria

Answer / Solution

Answer / Solution

Number of turns on the solenoid = 15 turns/cm = 1500 turns/m (convert per cm to per m by dividing 100)

Number of turns per unit length, n = 1500 turns

The Solenoid has a small loop of area, A = 2 cm^{3} = 2 x 10 ^{-4} m^{2}

Also, Current carried by the solenoid changes from 2 A to 4 A. Therefore change in current in the solenoid is given by Faraday's Las is given by the formula is

e = dφ/dt ........ (1)

where φ = Induced flux through the small loop = BA . . . (2)

Hence, equation 1 becomes

e = d/dt (BA)

= A μ_{0} n x (di/dt)

= 2 x 10^{-4} x 4π x 10^{-7} x 1500 x 2/0.1

= 7.54 x 10^{-6} V

Hence, the induced voltage in the loop is 7.54 x 10^{-6} V

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