Physics 014 Magnetic Fields

Topics Definition of B Circulating charged particles Force on a current carrying wire Torque on a current loop Magnetic dipole moments

B field Charges interact with electric fields but how do magnets work? The magnetic field (B)

B field For the electric field Electric charges Field everywhere in space

B field For the magnetic field Magnetic charges ? - NO Field everywhere ? - YES

B field No magnetic charges (magnetic monopoles) magnetic fields do effect charged particles

B field The force on a particle with charge q and velocity v in a fields B and E is

B field The SI unit for B is the tesla 1 tesla = 1 T =1 N/ (A m)

B field Another unit for B that is sometimes used is the guass 1 tesla = 104 gauss

B field How do you find the force on a particle?

B field How do you find the force on a particle?

??? A charged particle with velocity v travels through a uniform field B. What is the direction of the magnetic force FB on the particle?

B field Just as with the electric field, magnetic fields may be described by using field lines.

B field Magnetic field lines

B field Opposite poles attract, like repel

Circulating charges If a charged particle enters a uniform B field with a velocity perpendicular to the field, it will move in a circle.

Circulating charges

Circulating charges If particles are moving in a circle, the centripetal force is the magnetic force

Circulating charges For the period and frequency of the charge

??? For two particles (one proton the other an electron) traveling on circular paths each with the same speed in a uniform B field, which particle follows the smaller circle?

Force on a wire We’ve seen that magnetic fields exert forces on charged particles. They also exert forces on wires.

Force on a wire

Force on a wire In general, for a wire segment L , with current i and in a field B,

??? The figure shows a current i through a wire in a uniform magnetic field B and the force on the wire FB. The field is oriented so that the force is maximum. In what direction is the field?

Torque on current loop Consider what happens to a loop of current in a uniform magnetic field.

Torque on current loop Consider a rectangular loop of length a and width b carrying a current i, in a uniform magnetic field B. What is the torque that causes the loop to rotate?

Torque on current loop Forces due to sides 2 and 4 cancel out Sides 1 and 3 are perpendicular to B and yield a net torque

Torque on current loop If instead of one loop we had a coil of N loops,

Magnetic Dipole Moment We’ve seen that torque will rotate a coil in a uniform magnetic field. The current loop acts like a bar magnet and is said to be a magnetic dipole

Magnetic Dipole Moment Define the magnitude of the magnetic dipole moment (μ) as

Magnetic Dipole Moment The direction of the magnetic dipole moment is found with the right hand rule.

Magnetic Dipole Moment The torque on a current loop is then

Magnetic Dipole Moment The magnetic potential energy of the magnetic dipole in an external field is

Magnetic Dipole Moment Lowest energy = - μB Highest energy = μB

Magnetic Dipole Moment The work done on the dipole by the external field is

Magnetic Dipole Moment The work done by an external agent is the negative of the work done by the field. (dipole stationary before and after change)

??? For four orientations at angle θ of a magnetic dipole moment μ, rank the orientations according to (a) the magnitude of the torque on the dipole (b) the potential energy of the dipole, greatest first.