Magnetic Dipole Moment of a Current Loop and Bar Magnet

For numerical questions: note N, I, A, B, and theta; calculate m = NIA; if torque is asked, substitute in tau = mB sin theta; write SI units at each stage; interpret maximum or zero torque from the value of theta.

A useful diagram shows a current loop, direction of current, area vector perpendicular to the loop, and magnetic dipole moment along the area vector. For torque, show m making angle theta with uniform B.

Using tau = mB for every angle is wrong. tau = mB only for theta = 90 degrees; the general expression is tau = mB sin theta.

Magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic dipole. For a plane current loop, its magnitude is m = NIA.

Magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic dipole. For a plane current loop, its magnitude is m = NIA. Formula: m = NIA. Here m is magnetic dipole moment in A m^2, N is number of turns with no unit, I is current in ampere, and A is area in m^2. Torque in a uniform magnetic field is tau = m x B, with magnitude tau = mB sin theta, where B is magnetic field in tesla and theta is the angle between m and B. Use these formulas for current loops, coils, and equivalent dipole treatment of magnets in a uniform magnetic field. A circular coil with 50 turns, current 0.20 A, and area 4.0 x 10^-3 m^2 has magnetic dipole moment m = NIA = 50 x 0.20 x 4.0 x 10^-3 = 4.0 x 10^-2 A m^2.

A current-carrying loop behaves like a magnetic dipole. Its magnetic dipole moment depends on the number of turns N, current I, and area A of the loop. The direction of the dipole moment is perpendicular to the plane of the loop, given by the right-hand thumb rule. A bar magnet can also be treated as a magnetic dipole, with its dipole moment directed from south pole to north pole inside the magnet. Formula: m = NIA. Here m is magnetic dipole moment in A m^2, N is number of turns with no unit, I is current in ampere, and A is area in m^2. Torque in a uniform magnetic field is tau = m x B, with magnitude tau = mB sin theta, where B is magnetic field in tesla and theta is the angle between m and B. Use these formulas for current loops, coils, and equivalent dipole treatment of magnets in a uniform magnetic field. A coil of 100 turns has area 2.5 x 10^-3 m^2 and carries current 0.40 A. Find its magnetic dipole moment and maximum torque in a 0.20 T field. Calculation: m = NIA = 100 x 0.40 x 2.5 x 10^-3 = 0.10 A m^2. Maximum torque occurs when sin theta = 1, so tau_max = mB = 0.10 x 0.20 = 0.020 N m. Interpretation: the coil experiences maximum turning effect when its dipole moment is perpendicular to the field. Questions usually ask for the formula and unit of magnetic dipole moment, calculation of m for a coil, or torque on a magnetic dipole placed at an angle in a uniform magnetic field. Using tau = mB for every angle is wrong. tau = mB only for theta = 90 degrees; the general expression is tau = mB sin theta.