Magnetic field along axis of solenoid



A solenoid is a ling cylindrical coil having number of circular turns. Consider a solenoid having radius R consists of n number of turns per unit length. Let Pbe the point at a distance x̥ from the origin of the solenoid where we have to calculate the magnitude of the magnetic field. The current carrying element dx at a distance x from origin and a distance r from point P

Magnetic field along axis of solenoid

The magnetic field due to current carrying circular coil at any axis is

Magnetic field along axis of solenoid

from figure we have

Magnetic field along axis of solenoid

Now from above three equations, we get,

Magnetic field along axis of solenoid

Now total magnetic field can be obtained by integrating from Φ1 to Φ2, we get

Magnetic field along axis of solenoid

Hence this expression gives the magnetic field at point p of the solenoid of finite length.

For infinite long solenoidMagnetic field along axis of solenoid

so,

Magnetic field along axis of solenoid