Magnetic Force on Freely Moving Charges ELECTROMAGNETISM Magnetic Force on Freely Moving Charges

Important Facts about Fm Fm acts on the e¯ in wire, not on the wire itself ∴ the wire is not required for Fm to exist Fm acts on any moving charge.

Fm can act on any moving charge, even if it is not in a wire

Equation: q = magnitude of charge (C) v⊥ = speed of the charge, ⊥ to B field (m/s) B = external magnetic field (T)

perpendicular parallel

Ex. 2 A proton is moving 8. 60 × 104 m/s North through a 1 Ex. 2 A proton is moving 8.60 × 104 m/s North through a 1.20 T perpendicular magnetic field directed vertically upward. Find its acceleration (mag and dir).

Direction of a:

Magnitude of F:

Acceleration

Uniform Circular Motion If Fm is the only force on the charge

If Fm is the only force, then, Fm is Fnet

What is the direction of the acceleration? How do you know?

Newton's 2nd Law: a is in the same direction as Fnet

Notice that This is called centripetal acceleration.

Centripetal acceleration Change in direction, but no change in speed. Thus it is uniform circular motion.

Notice that both Fm and ac act toward the center of the circle Fm is called the centripetal force since it is responsible for moving the charge in a circle Notice that both Fm and ac act toward the center of the circle

Equation: