If the number of turns of a solenoid is doubled, keeping the other factors constant, how does the magnetic field at the axis of the solenoid change?

Explanation

`B_(1) = B` (say), `n_(1) = n, n_(2) = 2n, B_(2) = ?`
Magnetic field at the centre of a solenoid is given by `B = (mu_(0) n I a^(2) (2l))/(2r^(3))`
As I, `a^(2), 2l` and r are constants, `B prop n`
`rArr (B_(2))/(B_(1)) = (n_(2))/(n_(1)) rArr (B_(2))/(B) = (2n)/(n)`
`:. B_(2) = 2B`