# Work done by an Electric Field Clarification

Hi,

I'm trying to conceptualize the idea of work done by an electric field, can someone let me know if my reasoning is right?

For a +ve charge, if it is moved against the electric field, the Electric Field does -ve work (W=-PE = -qV = (-)(+)(-))

For a -ve charge, however, if it is moved against the electric field (i.e.e to an area of higher electrical potential), the work done by the electric field must be +ve since PE=qV, and q is -ve, V is +ve, and thus PE is -ve. However, since Work by the field=-PE, the work must then be positive.

My reasoning for moving the negative charge is the one I'm kind of iffy about, since one might think moving a charge against the field would imply that work done by the field is negative.

However, since a negative charge has a tendency to spontaneously move towards an area of higher potential, it makes sense that moving towards an area of lower potential (i.e. against the Electric field lines) means work done by the field is positive.

Can anyone help me out on this?

Thanks alot.

Defennder
Homework Helper
For a +ve charge, if it is moved against the electric field, the Electric Field does -ve work (W=-PE = -qV = (-)(+)(-))
Yes, but you could have written it as W = qV where V is the positive potential difference and the minus sign is due to the fact we are looking from the perspective of the field and not the amount of work we must do to move the charge.

For a -ve charge, however, if it is moved against the electric field (i.e.e to an area of higher electrical potential), the work done by the electric field must be +ve since PE=qV, and q is -ve, V is +ve, and thus PE is -ve. However, since Work by the field=-PE, the work must then be positive.
Yes, again like above, the work done is W = -q(V), which is negative from perspective of an external force. From the field perspective, it then doing positive work.

My reasoning for moving the negative charge is the one I'm kind of iffy about, since one might think moving a charge against the field would imply that work done by the field is negative.

However, since a negative charge has a tendency to spontaneously move towards an area of higher potential, it makes sense that moving towards an area of lower potential (i.e. against the Electric field lines) means work done by the field is positive.
That is true for positive charges, but not for negative charges. Just think about whether you'll have to exert any force to make the negative/positive charge move towards or away from a region of higher/lower potential. If the displacement of the charge is opposite to the direction of applied electric field force, then the field is doing negative work on it. Just keep in mind the mathematical definition of work done by a force and you'll understand it.

i think that, for W=-q (delta V)

holds for, charge moved from higher potential to lower, or from lower to higher, CONSIDERING THAT THE FIELD IS DOING THE WORK.

If the Field does work in moving the charge away. (to a lower potential) then its clear that the work is positive , since the electric force and the distance moved are in the same direction.

This fact is also confirmed by ur W=-q(delta V)

because here (Delta V) will be negative and the two minuses will cancel each other and we are gonna be left with positive work