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  • A long solenoid of diameter 0.1 m has 2 x 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid a

A long solenoid of diameter 0.1 m has 2 x 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10\pi ^2 \Omega, the total charge flowing through the coil during this time is:

Option: 1

32\pi \mu \text{C}


Option: 2

16 \mu \text{C}


Option: 3

32 \mu \text{C}


Option: 4

16\pi \mu \text{C}


Answers (1)

best_answer

Field at center of solenoid = B=μ0?Nl?i     where, Nl?-number of turns per unit length
Flux through the inner loop = 100 \times \pi 0.01^2 B =100 \times \pi 0.01^2 \times \mu_0 N_l i


emf induced = rate of change of flux =\frac{ \triangle \phi}{\triangle t } = 100 \times \pi 0.01^2 \times \mu_0 N_l \frac{\triangle i}{\triangle t}


Current through loop =i=\dfrac{emf}{R} = \frac{ \triangle \phi}{\triangle t } = 100 \times \pi 0.01^2 \times \mu_0 N_l \frac{\triangle i}{\triangle t} \frac{1}{R}



Total charge through the coil during this time=i \triangle t = \frac{ \triangle \phi}{\triangle t } = 100 \times \pi 0.01^2 \times \mu_0 N_l \triangle i \frac{1}{R} = 3.2 \times 10^{-5} C

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