Combining Electric and Magnetic Forces

Claimed by Alana Kaplan

When a charged particle is moving through a space with present electric and magnetic forces, if the forces are not balanced, the particles trajectory will change. It is important to remember that though the forces, observably, interact with a particle in different patterns, their effects can be quantitatively be compared.

Electric Forces:

Qualitative:

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Figure 1. An electric force acts in a pattern parallel to the electric field, pointing radially inward or outward of a particle. The direction depends on the signs of the interacting charged particles.

Figure 2. Magnetic Fields follow a helical pattern

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Figure 3. Magnetic Force Right Hand Rule

• A particle being acted upon by an electric force will move in a straight line, in the path, or negative path depending on charge, of the the electric field line (See Figure 1) .

• Electric fields point in a direction radially outward/ inward of a charged particle. There are four possible scenarios for the interaction of 2 charged particles:

1) A (-) charged Particle(1) is acting on a (-) charged particle(2)

• Particle(2) feels force pointing radially outward from Particle(1)

2) A (+) charged Particle(1) is acting on a (-) charged particle(2)

• Particle(2) feels force pointing radially inward toward Particle(1)

3) A (-) charged Particle(1) is acting on a (+) charged particle(2)

• Particle(2) feels force pointing radially inward toward Particle(1)

4) A (+) charged Particle(1) is acting on a (+) charged particle(2)

• Particle(2) feels force pointing radially outward from Particle(1)

Quantitative: The electric force formula is as follows:

Where 1 is the electric field from the source and 2 is the charge of the particle feeling the source

• Note that electric forces can perform work

Magnetic Forces:

• The magnetic force on a charged particle is orthogonal to the magnetic field.

• The particle must be moving with some velocity for a magnetic force to be present.

• Particles move perpendicular to the magnetic field lines in a helical manner (See Figure 2)

• To find the magnetic force, you can use the Right Hand Rule as follows (See Figure 3):

1) Thumb in direction of the velocity

2)Fingers in the direction of the magnetic field

3) Your palm will face in the direction of the Magnetic Force

Quantitative:

Magnetic and Electric Forces together:

The net force acting on a particle passing through a magnetic and electric field is:

This formula is known as "Lorentz Force":

When the net force is equal to zero, the velocity stays constant.

As seen in Figure 4 , when the net forces acting on a particle are balanced the electric field, magnetic field, and velocity vector are all perpendicular to each other. The electric and magnetic forces are equal but opposite.