Faraday’s E&M Fields

Example 3: Kinetic Energy of a Charge in a Field

The Question:

Electrified fruits and vegetables.

In fake units, pretend that the electric field in the figure above has a magnitude of $E=5$. 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: $m_A = 4m_B$.

1. What directions are the forces on the charged apple and broccoli?

2. What is the force on the broccoli and apple in fake units?
3. What is the kinetic energy gained by each after then have experienced that force for a distance $d$?

The Answer:

The positive charge will go in the direction of the electric field vector (or here, toward the negative plate) and the negative charge will do the opposite.

1. So the apple experiences a force that’s down and the broccoli, a force that’s up.

The magnitude of the forces is generally: $F=qE$, so:

2. $F(\text{apple})=q_A E = 4\times 5 = 20$

   and
   $F(\text{broccoli})=q_B E = 2\times 5 = 10$

So even though the apple is much more massive…the force is independent of that.

The kinetic energy is in general, $K=qEd$ so:

3. $K(\text{apple}) = q_A Ed = 4\times 5d = 20d$

   and
   $K\text{broccoli}) = q_B Ed = 2\times 5d = 10d$