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 P be 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-solenoid1

from figure we have



Now from above three equations, we get,

Magnetic-field-along-axis-of-solenoid3

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

Magnetic-field-along-axis-of-solenoid4

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

so,