Force on a Moving ChargeA charged particle experiences a force when moving at a non-zero anglewith respect to a magnetic field. The force on the charge is greatest when It moves perpendicular to the magnetic field.

F=qvB sinθ

q = the amount of charge in motion in the magnetic fieldv = the velocity the charge in the magnetic fieldB = the magnetic field strengthθ = the angle between the velocity direction and magnetic field

Direction conventions:

x: into the page (-z) •: out of the page (+z)

x x x

x x x

x x xField lines out of the page

B

Field lines into the page

Bv

velocity out of the page

F x

force into the page

•The force, charge velocity direction, and magnetic field direction are all perpendicular to each other.• There is no force on a charge that moves parallel to a magnetic field.

First Right Hand Rule

velocityforce

magnetic field

• Used to determine the velocity direction, force direction, and magnetic field direction for a charge in motion in a magnetic field.• The right hand rule is used for positive charges.

Example Problem

• A proton moves at 3.0x105 m/s in the positive-x direction while a 4.5 T magnetic field acts in the negative-y direction. What is the magnitude and direction of the force exerted on the proton?

F=qvBsinθ=(1.6x10-19C)(3.0x105 m/s)(4.5 T) sin90°=2.2x10-13 N

• Use the first right hand rule to determine the force direction on the charge.

• -z direction

What is the resulting motion of a charge in a magnetic field?

v

F

-

What is the direction of the magnetic field surrounding the charge?

Force on wire in a magnetic field

+ + + + + ++

I

A current in a wire constitutes charges in motion.

F = qvBsinθ =q(L/t)B sinθ = (q/t)LBsinθ = BILsinθ

L

F=BILsinθ F=force on the wire from the external magnetic fieldB = The external magnetic field that surrounds the wireI = current in the wire L=length of wire in the magnetic fieldθ = angle between the current direction and magnetic field.

The direction of the magnetic field can be determined by the right hand rule withthe current I, replacing the velocity direction.

Example problem

• A wire length carries 6.5 A of current along the positive-x axis while in a magnetic field of 7.0 T directed towards the positve-z axis. A length of 18 cm of wire is exposed to the magnetic field. What is the magnitude and direction of the force on the wire?

• F=BILsinθ = (7.0 T)(6.5 A)(.18m)sin 90°• F=8.2 N

• Use the right hand rule to determine the direction of the force.

• Force direction: -y

An Applications of Force on a Wire –Simple Internal Diagram of an Electric Motor

Motor – a device which converts energy to mechanical motion

Metal brushes inside ring

S N

I I

•x