# Calculating change in current in a solenoid

## Homework Statement

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.

## Homework 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}##

## 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.