# Keeping the total length of coil unchanged, the no. Of rounds in the coil are doubled. Its new self inductance will be 1.  Four times. 2.  Double 3. Half. 4. Unchanged

ASHISH KUMAR
27 Points
11 months ago
magnetic field for solenoid = B = $\mu$NI
and formula for self inductance is
N$\phi$ = L I  ( where L is self inductance )
and $\phi$(flux) = BACos $\theta$  ( $\theta$ = 0 so Cos $\theta$= 1)
case 1 )  N ( $\mu$NI * A) = LI
L = $\mu$ N^2 A
case 2)  now no of turn is doubled
so 2N ( $\mu$(2N) I *A ) = L' I
L' = 4 $\mu$N^2 A
hence  Its new self inductance will be four times
option 1 Four times is correct