How much work does the electric field do in moving a -7.7 `muC` charge from ground to a point where potential is +55 V higher?

ishpiro | Certified Educator

The potential difference between the two points, or voltage `Delta V,`is defined as the work it would take to move a positive unit charge from the first point to the second, AGAINST the electric force provided by the field. Note that the work in this definition is done by some outside agent, not the electric field.

The work it takes to move any charge through potential difference `DeltaV` is then

`W=qDeltaV`

The work done by the electric field is the opposite of this quantity:

`W_field=-qDeltaV`

Plugging in the values of charge and voltage given in the problem, the work done by the electric field is

`W_field=-(-7.7muC)(5.5V)=42.35muJ`

Note that the work done by the field is positive. This makes sense because a negative charge placed in the electric field will move towards the point with higher potential, so that its potential energy will decrease.