Question

A magnetic field of $4\times {10}^{-4}Wb$ is linked with each turn of a coil having $200$ turns when there is electric current of $2A$ in the coil. the self inductance of the coil is: (area of is $2{cm}^2$):

• A. $20\mu H$
• B. $8\mu H$
• C. $4\mu H$
• D. $30\mu H$

Answer 1

The correct option is C $4\mu H$

The inductance of the coil numerically equal to emf induced in the coil when the current in coil changes at the rate of 1 A/s. If 'I' is the current flowing in the circuit, then flux linked with the circuit is observed to be proportional to 'I', i.e

$\varphi \propto I$

$\varphi =LI..........\left(i\right)$

where L is the self inductance or coefficient of self inductance or simply inductance of coil

Net flux through the solenoid,

$\varphi =200\times 4\times {10}^{-4}=8\times {10}^{-2}wb$

Now, putting in equation (i)

$8\times {10}^{-2}=L\times 2$

$L=4\mu H$