Question

Derivation of Potential energy of Magnetic field ?
Can any one derive it for me

Answer 1

Hi
Derive potential energy of Magnetic field ?

Answer 2

Potential energy of magnetic field can be derived by using the using a magnetic dipole kept in the magnetic field.

See, there is a torque which tries to align the dipole along magnetic field.
The torque is \(\tau = mBsin \theta\)
Work done to rotate the dipole by \(d\theta\) against the torque is
\[dW = \tau d\theta = mBsin \theta d\theta\]
Potential energy \( U = \int_{\theta_0 = 90^o}^{\theta} mBsin \theta d\theta = -mBcos\theta = -\vec{m}.\vec{B}\)
By convention it is assumed that at \(\theta_0 = 90^o,\ U = 0\)