Magnetic Dipole Field at Pole

\[B=\frac{\mu_0 m}{2\pi r^3}\]

Variables

Bmagnetic field strength at pole (T)

mu0vacuum permeability (H/m)

mmagnetic dipole moment (A·m²)

rdistance from dipole center (m)

Description

What is this formula?

This formula calculates the magnetic field strength generated by a magnetic dipole at a point located along the dipole axis, commonly called the pole direction.

When to use it

Use this equation when evaluating magnetic fields on the axial line of a dipole, such as near the poles of a bar magnet or along the Earth's magnetic axis.

Example

A magnetic dipole has a magnetic moment of 180 A·m². Calculate the magnetic field at a point located 0.25 m from the center along the dipole axis.

Data:

m = 180 A·m²

r = 0.25 m

mu0 = 4π × 10^-7 H/m

Formula:

B = (mu0*m)/(2*pi*r^3)

Substitution:

B = ((4*pi*10^-7)*180)/(2*pi*(0.25^3))

Result:

B = 2.30 × 10^-3 T

Applications

- Earth's polar magnetic field estimation

- Magnetic dipole modeling

- Electromagnetic simulations

- Magnet design

- Magnetic sensor analysis