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A uniform electric field points along the z-direction. Over what region is the electric potential constant?

1. on the x-y plane for a given z
2. throughout all space
3. for any x at a fixed z (one-dimensional only)
4. for any y at a fixed z (one-dimensional only)

Correct answer: on the x-y plane for a given z

Solution

For a uniform field E along z, V = -E*z + constant, so V depends only on z. Every plane of constant z (an x-y plane) is an equipotential. Thus the potential is constant over the whole x-y plane at a given z, not just along a single line.

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