# Integrate the on axis field of finite solenoid from a thin shell one, HELP!

1. Aug 13, 2009

### demon_samuel

Dear all,

i met a problem that i couldn't get the on axis field of a finite solenoid that integrating from a thin shell solenoid equation.

http://www.netdenizen.com/emagnet/solenoids/thinsolenoid.htm

And the on axis finite solenoid equation link:
http://www.netdenizen.com/emagnet/solenoids/solenoidonaxis.htm

If i was right, the integral of (a/sqrt (a*a+r*r)) dr should be a*ln(r+sqrt(r*r+a*a)), if so i couldn't figure out how to get the (r2-r1) term in the second link equation.

Samuel

2. Aug 13, 2009

### kuruman

To get the second expression from the first, you need to integrate over dr from r1 to r2. You do this by adding "solenoids" of radius r, thickness dr, and length l carrying current di. According to the first expression, the contribution from one such solenoid is

$$dB = \frac{\mu_{0}N di}{2 l}[\frac{x_{2}}{\sqrt{x^{2}_{2}+r^{2}}}-\frac{x_{1}}{\sqrt{x^{2}_{1}+r^{2}}}]$$

Before you integrate, you need to express di in terms of dr. Hint: Think in terms of current density.

3. Aug 13, 2009

### demon_samuel

Thank you very much, i got the answer.