## Magnetic Force on a Moving Charge

A charge moving in a magnetic field experiences a force in the same way that a current moving in a magnetic field experiences a force ā a current is after all, a collection of moving charges.

The magnitude of the force F on a moving charge is found to be proportional to

• the magnitude of the magnetic field

• the magnitude of the charge

• the speed of the charge

• the sin of the anglebetween the direction in which the charge is moving and the field.

We can write F=Bqv sin %theta .

We can use this equation to give a definition of the magnetic field strengthThe magnetic force is at right angles to both the direction of movement of the charge and the magnetic field. This is implied by Fleming's left hand rule. This makes circular motion possible ā the magnetic force is at right angles to the motion in the same way as the force of gravity is at right angles to the motion of planets in circular orbits around the Sun.

We can find the radius of the orbit by equating the centriptal to the magnetic force.