Faraday’s E&M Fields

Example 2: Vector Electric Forces

The Question:

The force on an electric charge of magnitude $q$ in an electric field, $E$ is:

Notice that there’s nothing in this equation that involves the masses of the objects…only their charge matters.

Here, the charges for the broccoli and apple are: $q_B=+2$ and $q_A=-4$. Let’s say that the mass of the apple is four times that of the broccoli: $m_A = 4m_B$.

So continuing the fake units of $qE$ for the force, draw a vector length that is scaled so that the length of a force of magnitude $1E$ and then draw the force vectors on the apple and the broccoli corresponding to the above configuration.

The Answer:

The direction of the force on the negative apple will be…up and that for the broccoli, will be down. And since the magnitude of the apple’s electric charge is twice that of the broccoli, it’s force vector will be twice as long. Like this:

(Notice that the length of the force vectors is just an overlay on top of the picture of the plates…the dimensions of the spacing haven’t anything to do with the length of force vectors.)