When number of turns per unit length of a solenoid is doubled, its self inductance becomes:

CONCEPT:

• Self-Induction: Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.
  • As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
  • This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.

Self-inductance of a solenoid is given by:

 -- (1)

Where μo = Absolute permeability, N = Number of turns, l = length of the solenoid, and A = Area of the solenoid.

EXPLANATION:

 μo ,I, A are constants. So, we can say that 

L = k N² -- (2)

k is constant, N is the number of turns

L is directly proportional to the square of a number of turns.

If number of turns becomes N' = N², then inductance 

L' = k N' ² 

⇒ L' = k (2N)² = k 4 N² = 4 K N²

⇒ L' = 4 L

So, the inductance is increased by 4 times.

Hence the correct option is 4 times.

Important Points

Induced e.m.f can be given as