If potential is constant in a region, must the electric field be constant?

[Physicsisfun2005]

Nice AP Phyiscs prob.
If V (elec. potential) equals a constant throughout a given region of space, what can u say about E (Elec. field strength) in that region?

I think its also constant ;) ...but i was woderin if i was right

 

[Tide]

Yes the electric field is constant - but a very special one! Hint: How do potential and electric field relate to each other? :-)

 

[Physicsisfun2005]

Is it some type of direct variation?...

I have something in my notes (a mess lol) where the V vs r and E vs r graphs are related...E at a certain point is the slope of the V vs r graph at that point.

 

[HallsofIvy]

The difference between potential at two points is also the work done by a force moving an object from one point to the other. If the potential is a constant what is the force necessary to move an object from any point to any other?

 

[Physicsisfun2005]

If the potential is a constant the force necessary to move an object from any point to any other would be 0. B/c no work is done and then there would be a potential difference. In this instance I not sure how u would NOT do work if u had a force involved.

 

[HallsofIvy]

Exactly! Therefore the force MUST be ___.

 

[Physicsisfun2005]

zero...I figure E=0...b/c dV=Edr