Important Equations

Magnitude of the Magnetic Force on a Moving Charged Particle (q)

F = qvB sinθDirectional right-hand force rule for

moving charges: - when the fingers of the right hand are pointed in the direction of v and then curled, the extended thumb points in the direction of the force F on a positive charge. (F is in the opposite direction for a negative charge.)

Magnitude of the Magnetic Field near a Long, Straight, Current-Carrying Wire:

B = μ0I/2πd (where μ0 = 4π x 10-7T.m/A, called the magnetic permeability of free space)Directional right-hand source rule: - when a current carrying wire is grasped with the right hand, the extended thumb pointing in the direction of the current, the curled fingers indicate the directional sense of the magnetic field.

Magnitude of the Magnetic Field at the Center of a Circular Loop of Current-Carrying Wire:

B = μ0I/2rMagnitude of the Magnetic Field at the

Center of a Solenoid (along the axis): B = μ0NI/L or B = μ0nL

(where n = N/L)Magnitude of Force on a Straight, Current-

Carrying Wire: F = ILB sinθ

Directional right-hand force rule for a current-carrying wire:

- when the fingers of the right hand are pointed in the direction of the conventional current I and then curled toward the B vector, the extended thumb points in the direction of the force on the wire.Magnitude of Torque on a Single Current-

Carrying Loop: τ = IAB sinθ (where IA is called the magnetic moment, m, of the loop: m = IA)

Magnitude of Torque on a Current-Carrying Coil (of N Loops):

τ = NIAB sinθ