Question

State the condition for which magnetic potential energy of a dipole is a) Minimum b) Maximum​

Answer 1

a)minimum

or

b)maximum

Answer 2

State the condition for which magnetic potential energy of a dipole is

1. minimum
2. maximum

solution : let's derive the equation of potential energy of a dipole.

consider a dipole of dipole moment p is placed in a electric field E. owing to inclination of dipole with electric field, it rotates.

let τ is an external torque acting on the dipole to neutralise its rotation from θ₀ to θ₁.

now the work done by the external torque in the dipole , W = $\int\limits^{\theta_1}_{\theta_0}{\tau}\,d\theta$

here τ = PE sinθ

so, W = PE(cosθ₀ - cosθ₁)

we know, the work done is stored as potential energy.

to choose reference angular position of dipole, θ₀ = π/2 and θ₁ = θ

then, U = PE(cosπ/2 - cosθ) = -PEcosθ

so potential energy of a dipole is -PEcosθ

at θ = π ⇒U = -PEcosπ = PE [ maximum ]

at θ = 0⇒U = -PEcos0 = -PE [ minimum ]