# Formula for magnetic field of solenoid

1. Feb 2, 2005

### Gosuto Inu

Hi!
I need formula for magnetic field of solenoid on axis of solenoid in some distance from center.Also I need something about interaction magnetic field on material point(interaction solenoid on material point).I want to know force that infuence on material point. Thx in advance and sry for my bad english :tongue:

2. Feb 2, 2005

### Andrew Mason

The field at the center is:

$$B = k\mu_0 In/L$$

where B = magnetic field; I = current; k = permeability constant $\mu/\mu_0$; and n = number of turns; L = length of solenoid.

To find the B at a distance from the center you have to apply the Biot-Savart law which is pretty complicated for a solenoid. You have to integrate the contributions from all the current elements of each loop. At a large distance from the center (large compared to the length and diameter of the solenoid) it would be something like:

$$B = \frac{\mu R^2nI}{2d^2}$$

where R is the radius of the solenoid; d is the distance away; n is no of turns;

AM

Last edited: Feb 2, 2005
3. Feb 4, 2005