The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field ( vecB) having magnetic moment ( vecm) will be

Question

The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field ( vecB) having magnetic moment ( vecm) will be (A) -mB, zero (B) mB, zero (C) zero, mB (D) zero, -mB

Tardigrade Admin · Accepted Answer

Torque, vecτ = vecm × vecB = mB sin θ and magnetic potential energy Um = vecm. vecB = mB cos θ at θ = 0° the dipole will be in most stable position τ = mBsinθ = mBsin 0° = 0 and Um = -mB cosθ = -mBcos 0° = - mB

Q. The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field $(B)$ having magnetic moment $(m)$ will be

-mB, zero

mB, zero

zero, mB

zero, -mB

Torque, $τ = m \times B = m B s in θ$
and magnetic potential energy $U_{m} = m . B = m B cos θ$
at $θ = 0^{\circ}$ the dipole will be in most stable position
$τ = m B s in θ = m B s in 0^{\circ} = 0$
and $U_{m} = - m B cos θ = - m B cos 0^{\circ} = - m B$

Q. The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field (B) having magnetic moment (m) will be