Calculating Magnetic Field of a Solenoid with Changing Amperage

[GermanMC]

Homework Statement

I've been given a solenoid and I have N/l = 100 turns/meter, dI/dt = 0.05A/s and a radius of 0.005m. I am only concerned with the dI/dt.

Homework Equations

B = μ*N/l*I
$\Phi$ = $\int\int$ B$\bullet$n dl
$\epsilon$ = d$\Phi$/dt

The Attempt at a Solution

For B I get the field but how do I deal with my amperage in amps/s instead of just amps. Once I get that I'll take the derivative of the flux with respect to time and I'll be fine. Any clues will be much appreciated.

 

[marcusl]

When you take d(phi)/dt of your 2nd expression, you can interchange the order of differentiation and integration because both are linear operations. d/dt comes inside and operates on B. You find dB/dt from your first expression, which looks wrong BTW. (Shouldn't I be in the denominator?)