A very long solenoid (axis along z-direction) of n turns per unit length carries a current that increases linearly with time, `I=Kt`. What is the magnetic field inside the solenoid at a given time t? [JEST 2019]

Problem: A very long solenoid (axis along z-direction) of n turns per unit length carries a current that increases linearly with time, `I=Kt`. What is the magnetic field inside the solenoid at a given time t? [JEST 2019]

(A)`B=mu_0nKthatz`     (B)`B=mu_0nKhatz`    (C)`B=mu_0nKt(hatx+haty)`    (D)`B=mu_0nKthatx`

Answer:

The magnetic field of a long solenoid at any instant t is given by 

`B=mu_0nI(t)hatz`

so, `B=mu_0nKthatz`

Option (A) is correct.