Magnetic Field Magnetic fields are produced by electric currents, which can be

macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz force law. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole. The SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law Fmagnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss).

Lorentz Force Law

The electric force is straigtforward, being in the direction of the electric field if the charge q is positive, but the direction of the magnetic part of the force is given by the right hand rule.

Earth Source

Magnetic Force

The direction of the cross product can be obtained by using a right-hand rule: FINGERS of the right hand point in the direction of the FIRST vector (v) in the cross product, then adjust your wrist so that you can bend your fingers (at the knuckles!) toward the direction of the second vector (B); extend the thumb to get the direction of the force.

Magnetic Field

Magnetic Flux

.cosd BdAff=

Centripetal Force due to B

A charged particle moving in a plane perpendicular to a magnetic field will move in a circular orbit with the magnetic force playing the role of centripetal force. The direction of the force is given by the right-hand rule. Equating the centripetal force with the magnetic force and solving for R the radius of the circular path we get

Van Allen radiation belts around the Earth

The Earth's surface and its inhabitants are protected from dangerous cosmic radiation (energetic protons) from the Sun by the Earth's magnetic field. Using the right-hand rule one can see that positively charged particles coming from the Sun will be deflected in an easterly direction.

Charge moving under B

An electric field and a magnetic field placed at right angles to each other can function as a "velocity selector." When the force up = force down in (b) above, the charge will travel in a straight (horizontal) line. The speed can be obtained from the equation

.

/

qv xB q E

v E B

=

=

r ur ur

Speaker’s Vibrating Force

magnetic moment in machines

Couple Forces

Torque in Solenoid

Torque xBt m= =

Electrodynamics

Torque xBt m= =

Bullet Train

The force (F = I L x B) on the moving charges in the purple bar cause the bar to move to the right - a linear motor! Use the right hand rule to obtain direction of force on the moving charges (current) in the purple bar.

B caused by Current in a rod

Magnetic field B due to long straight current-carrying wire. Use a right hand rule to get the direction of the infinitesimal dB.

B around current carrying wire

Magnetic field B lines around long straight conductor. Note the use of the right hand rule to get the direction of the current.

Force on the conductor due to B

Parallel conductors carrying currents in same direction. The current I' is moving in the B field caused by the current I, so it experiences a force (F = I' L x B).

Force due to circular current

Magnetic field B caused by circular current loop. After adding (integrating) all the vector components caused by all the infinitesimal I dl the total B field will be in a direction along the x-axis. From symmetry we can see that the vectors components in the yz-plane will all cancel leaving only the component of B in the x-direction.

Magnetic dipole moment

I Am=ur rMagnetic dipole moment

( ) of an orbiting electron. The right-hand rule determines the direction of the magnetic moment of a current-carrying loop. The direction of the electron's angular momentum vector can be obtained using the right hand rule for angular

Lr

Charging current as source of B

The displacement current, as the capacitor is charged by Ic, can be regarded as the source of the B field.