# Calculating change in current in a solenoid

1. Apr 17, 2016

### redsox133

1. The problem statement, all variables and given/known data
A long, thin solenoid has 400 turns per meter and a radius of 2.65 cm. The current in the solenoid is increasing at a uniform rate dI/dt, and the induced electric field at a point near the center of the solenoid and 3.25 cm from its axis is 5.00✕ 10-6 V/m. Calculate dI/dt.

2. Relevant equations
$B_s = u_onI$
$N\frac{d\phi}{dt}=M\frac{dI}{dt}=\mathcal{EMF}$
$\oint \vec E \cdot d \vec L = \frac{dB}{dt}$

3. The attempt at a solution
I tried solving for $\frac{dB}{dt}$ using the third equation. I ended up with $E=\frac{r}{2}\frac{dB}{dt}$, and then I plugged in E and r to solve for $\frac{dB}{dt}$. I wanted to use that to solve for $\frac{dI}{dt}$ in the second equation but I don't know what M is. After that I tried taking the derivative of the first equation to get $\frac{dB}{dt}=u_on\frac{dI}{dt}$ and then solving for $\frac{dI}{dt}$ but I got the wrong answer. If someone could let me know if I'm on the right track I would appreciate it.

2. Apr 22, 2016