D.3 Motion in electromagnetic fields

What is the path of a charged particle moving into a uniform electric field perpendicular to its motion?

The particle follows a parabolic path because it experiences a constant electric force in one direction.

What is the path of a charged particle moving into a uniform magnetic field perpendicular to its motion?

The particle follows a circular path because the magnetic force acts as a centripetal force, always perpendicular to the velocity.

Why does the kinetic energy of a charged particle remain constant in a magnetic field?

The magnetic force is always perpendicular to the velocity, so it does no work on the particle and cannot change its speed.

What is the formula for the force on a charge moving in a magnetic field?

Force equals charge times velocity times magnetic flux density times the sine of the angle between the velocity and the field.

How do you calculate the force on a current-carrying conductor in a magnetic field?

Force equals magnetic flux density times current times length times the sine of the angle between the conductor and the field.

What is the force per unit length between two parallel current-carrying wires?

Force divided by length equals the permeability of free space times the product of the two currents, divided by the quantity two times pi times the distance between the wires.

When is the force between two parallel current-carrying wires attractive?

The force is attractive when the currents in both wires are flowing in the same direction.

How can the charge-to-mass ratio of a particle be determined from its motion in a magnetic field?

By equating the magnetic force to the centripetal force and solving for charge divided by mass using the radius of the circular path and the particle's speed.

What is the motion of a particle in perpendicularly oriented (crossed) electric and magnetic fields?

If the electric and magnetic forces are balanced, the particle will move in a straight line at a constant velocity.

How do you find the direction of the magnetic field around a straight wire?

Using the right-hand grip rule: thumb points in the current direction and fingers curl in the direction of the magnetic field lines.