What is a Solenoid?

It's a long wire coil wrapped in a cylindrical shape very tightly. The electric current that flows through the wire creates a magnetic field. Solenoids are generally electromagnets, inductors, and can be used as switches.

Magnetic Field in a Solenoid

The magnetic field inside a solenoid is parallel and uniform about the axis of the solenoid. The strength of the magnetic field in the solenoid depends on various aspects: the flowing current through the wire and the turns within the coil.

Formula 

The formula for the magnetic field of a solenoid is given by,

B = μoIN / L

Where,

N = number of turns in the solenoid

I = current in the coil

L = length of the coil.

Note: The magnetic field in the coil is proportional to the applied current and number of turns per unit length.

Solved Examples

Example 1: Calculate the magnetic field created by the solenoid of length 80 cm provided that the number of turns of the coil is 360, and the current passing through is 15 A.

Solution:

Given,

No. of turns N = 360

Current I = 15 A

Permeability μo = 1.26 × 10−6 T/m

Length L = 0.8 m

The magnetic field in a solenoid is given as, 

B = μoIN / L

B = (1.26×10−6 × 15 × 360) / 0.8

B = 8.505 × 10−3 N/Amps m

The magnetic field due to the solenoid is 8.505 × 10−4 N/Amps m.

Example 2: A solenoid with diameter of 40 cm generates a magnetic field of 2.9 × 10−5 N/Amps m. If it consists of 300 turns, calculate the current flowing through it.

Solution:

Given,

No of turns N = 300

Length L = 0.4 m

Magnetic field B = 2.9 × 10−5 N/Amps m

The formula for the magnetic field is

B = μoIN /L 

The formula for the current flowing through the coil is

I = BL / μoN 

I = (2.9×10−5 x 0.4 )/ (1.26×10−6 × 300)

I = 30.6 mA

 

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