If electric potential is constant throughout in a region of space what will be the electric field in this region?

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The Electric field is defined as the gradient of the electric potential. The electric potential is a scalar field, that is it has no direction, only measured values at each point.

In vector calculus, the gradient of a scalar field is a vector field which points in the direction of...

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The Electric field is defined as the gradient of the electric potential. The electric potential is a scalar field, that is it has no direction, only measured values at each point.

In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.

If the electric potential is constant, say 1 V, then there is no direction of greatest increase. Hence the gradient of the electric potential is zero, and the electric field is zero everywhere inside the region of constant electric potential.

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