How Does Electric Field Direction Relate to Equipotential Lines?

[bbuilder]

Homework Statement

The equipotential curves in a certain region of an equipotential diagram in an xy plane are parallel to the y-axis and are equally spaced. The potential is increasing in the +x direction. Which direction would an electric field vector point in this region?

Homework Equations

N/A

The Attempt at a Solution

The equipotential lines are vertical, so the electric field lines must be in the x-direction since they run perpendicular to each other. Would they point in the positive x direction since the potential is increasing there? I'm having a hard time picturing what this would look like.

 

[Adithyan]

Try to relate electric field and potential/potential difference- is there any formula by which potential can be written in terms of electric field? Think about it and let me know if you have any question.

Best of luck!

 

[bbuilder]

I know that V=∫Edl, but I'm having trouble connecting that to what the equipotential lines would look like.

 

[haruspex]

Would they point in the positive x direction since the potential is increasing there?

Suppose the field is created by some distant pair of opposite charges, one in positive x direction and one in the negative. Will the potential be higher towards the positive charge or towards the negative? Which way will the field point?

I know that V=∫Edl

No, it's V=-∫Edl. In differential form: E = -dV/dl (or -dV/dx in this context). You're told the potential increases with increasing x, so what is the sign of dV/dx?

 

[bbuilder]

Suppose the field is created by some distant pair of opposite charges, one in positive x direction and one in the negative. Will the potential be higher towards the positive charge or towards the negative? Which way will the field point?

No, it's V=-∫Edl. In differential form: E = -dV/dl (or -dV/dx in this context). You're told the potential increases with increasing x, so what is the sign of dV/dx?

The potential would be the same at both a positive charge and a negative charge because potential is scalar. The electric field would point towards the negative charge.

The sign of dV/dx is positive, but when the negative sign is taken into account then E is negative, so the electric field is going in the negative x-direction. Is this correct?

 

[haruspex]

The potential would be the same at both a positive charge and a negative charge because potential is scalar.

Eh?! Is +3V the same as -3V?

The electric field would point towards the negative charge.

The sign of dV/dx is positive, but when the negative sign is taken into account then E is negative, so the electric field is going in the negative x-direction. Is this correct?

Yes.