# Why are electric field lines also referred to as "lines of force"?

TypeFun

## Homework Statement

Why are electric field lines also referred to as "lines of force"?

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## Answers and Replies

TypeFun
Equipotential Lines

## Homework Statement

What are equipotential lines?
What is their relationship to electric fields lines?
Directions of electric fields are indicated by arrows, why are no directions indicated on equipotential lines?

## The Attempt at a Solution

Mentor
Two similar question threads merged.

On the Field/Force question, can you please show us the equation for the force on a charged object that is in an Electric field?

And on the Equipotential lines question, which way does the Electric field vector point, in relation to the Equipotential lines? Why do you think it points that way? Think about the force on the charged object question above...

TypeFun
E=F/q

By convention, the electric field vector points towards the negative and away from the positive. As far as I understand it, the decision for why an electric field vector points a certain way is a decision made by the person drawing the diagram

"Think about the force on the charged object question above..."
Are you referring to the equation that you asked for? In that case, the force is proportional to the electric field. Beyond that, I'm unsure how that relates to the direction of the equipotential lines.

Mentor
E=F/q

By convention, the electric field vector points towards the negative and away from the positive. As far as I understand it, the decision for why an electric field vector points a certain way is a decision made by the person drawing the diagram

"Think about the force on the charged object question above..."
Are you referring to the equation that you asked for? In that case, the force is proportional to the electric field. Beyond that, I'm unsure how that relates to the direction of the equipotential lines.

You wrote the correct equation, with the only thing to be added being that both F and E are vectors. So they point in the same direction.

Since forces do work, and since the force points in the same direction as E (for a positive charge in that E), the electric field E does no work on the test charge as it is moved orthogonally to the direction that the E field points in. Does that make sense? Work is force times distance (or Force vector dotted onto the path of movement), so if the movement is orthogonal to the Force vector, no work is done, and potential energy PE due to the E field is not changed.

So why are the equipotential lines always at right angles to the E field vector?