# Magnetic Field Formula

Magnetic field is a region surrounding a magnetic material or within a moving electric charge where the force of magnetism acts.  In other words, the force experienced by the field due to the magnet is known as magnetic force and this kind of field is known as magnetic field. Magnetic field varies from one shape to another just like solenoid has a different magnetic field than toroid.

There are three magnetic field formulas:

The magnetic field formula for current in an infinite straight filament is given by,

$B=\mu&space;_{0}i/2\pi&space;r$

Wherein,

B is the magnetic field,

r is the radius of the loop,

μ is the permeability constant, and

i is the current

Magnetic field formula in a solenoid is expressed by,

B = μo i n.

Wherein,

μo is the constant of permeability,

i is current in amperes,

n is the number of turns done by the wire per unit length of the solenoid,

Magnetic field formula in a toroid coil is given by,

B = μoiN / 2πr

Wherein,

B is the magnetic field in teslas,

i is the current in amperes,

N is the total number of turns made by the wire in the toroid

Example 1

Determine the magnetic field in a solenoid having 20 turns and current of 5 A.

Solution:

Given:

Number of turns, n = 20,

Current I = 5 A.

Magnetic field formula in a solenoid is given by,

B =  μo i n

= 1.26 × 10−6 H/m × 5 × 20

= 126 x 10-6 tesla

Example 2

A toroid of radius 5 cm has 30 turns. If a current of 5 A is passed through it, determine the magnetic field around it.

Solution:

Given:

No of turns, N = 30,

Radius r = 5 cm

= 0.05 m,

Current I = 5A.

Magnetic field formula in a toroid coil is given by,

B = μoiN / 2πr

= 1.26×10−6 × 5 × 30 / 2π × 0.05

= 1.504 x 10-6 tesla