Question

electric potential is constant in a region.what can you say about electric field?

Answer 1

We Know, E = - dV/dr

Since V is constant, electric field is zero.

Answer 2

Answer:

The E-field may or may not be zero in a region where E-potential is constant(same).

Explanation:

to explain this consider an equipotential surface between two oppositly charged || plates. Now we know that E-filed is not zero throught this region, rather then it has some valve, but at the same time we are sure that E-potential remains the same as we move across the equipotential surface (it is constant).

Thus one can say that, even in case of constant potential in a region E-field is not necessorilly zero.

Confusion:

     Now the confussion arises from the equation;

  E = - dV/dr

if V is constant then dV=0, which by putting in the above equation gives E=0.

In fact its not so, let's rewrite the equation as ;

dV=E.dr      (its the Dot product of E and r)

dV= Er cosθ

Now if dV = 0 then the equation becomes

0 = Er cos θ

Now, there are three possibilties,

Either      E = 0

or             dr = 0

or            cosθ = 0       (if θ between E and dr is 90°) as in the case of equipotential surface, where E is not zero but angle 'θ'

between E and dr is 90.