Question

under which condition electric intensity at a point is zero but electric potential is not zero. zero. and electric potential at a point is zero but electric intensity is not zero

Answer 1

Answer:

here's your answer

Explanation:

The short answer is YES. The potential can be non-zero at a point in a field where the field intensity is zero. Here is an analysis where I picked the geometry to make the calculation simple so I can determine the electric potential at a point where the electric field is zero.

Place two positive charges +Q on the x-axis at x = a and x = -a. Now I am going to bring a +1 C test charge along the y-axis from infinity to y = 0, the midpoint between the two positive charges +Q. First it should be clear that the field at the midpoint (x=0, y=0) is zero since the two charges have the same field intensity at that point but in opposite directions so that they cancel.

Now, the electric field at any point on the y-axis is

E(y) = 2Q/(4 Pi eo) x ( y/(a^2+y^2)^(3/2)) and the work done bringing the test charge in from infinity to the point (0,0) is integral [E(y) dy]. This integral is relatively easy and we get 2Q/(4 Pi eo) x ( 1/(a^2+y^2)^(1/2)). Putting in the limits, first y = infinity first and then y = 0 we get 2Q/(4 Pi eo) x ( 1/a) and the electric potential

V = -Integral{E(y) dy) = - Q/(2 Pi eo a).

So there is the answer. The electric potential at the midpoint between the two +Q charges where the electric field is zero is nonzero and negative. The minus sign says that you have to do work to bring the positive test charge to the zero field point from infinity.