Unit 4 Day 3 – Magnetic Dipole Moment & Applications Magnetic Torque Magnetic Dipole Moment Potential Energy of a Magnetic Dipole Magnetic Moment of a Hydrogen Atom Applications of magnetic Dipole Moment

Magnetic Torque When a loop of wire carrying a current is placed in a uniform magnetic field, the magnetic force will produce a torque on the loop, causing it to rotate This is the principle behind motors, analog voltmeters, and etc.

Magnetic Torque The torque on the dipole is: If the coil consists of N loops the current increases by N·I

Magnetic Torque If the coil makes an angle θ with the magnetic field, the magnetic force remains the same but the lever arm is reduced from ½b to ½bsinθ Torque is always in the direction of the net force Although this formula was derived for a rectangular coil, it is valid for any shape of flat coil

Magnetic Dipole Moment The quantity NIA in the torque formula is called the “magnetic dipole moment” Where the direction of A is in the direction of μ Therefore, in vector form, torque is expressed as:

Magnetic Dipole Potential Energy Remember the torque on an electric dipole: The electric potential energy of the electric dipole is: Hence, the magnetic potential energy of a magnetic dipole is:

Magnetic Moment of a Hydrogen Atom vt The hydrogen atom consists of a (-) charged electron orbiting a (+) charged proton The Coulombic force of attraction is the equivalent of the centripetal force keeping the electron in orbit FC

Applications of Magnetic Dipole Moment Electric Motors Voltmeter (Galvanometer) Loud Speaker