Consider a uniform electric field in the ẑ direction. The potential is a constant ______. a. in all space. b. for any x for a given z. c. for any y for a given z. d. on the x-y plane for a given z.

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b, c and d Explanation: We know, the electric field intensity E and electric potential V are E = - (dV)/(dr) Electric potential decreases in the direction of the electric field. The direction of electric field is always perpendicular to one equipotential surface maintained at the high electrostatic potential to another equipotential surface maintained at low electrostatic potential. The electric field in the z-direction suggests that equipotential surfaces are in the x-y plane. Therefore the potential is a constant for any x for a given z, for any y for a given z and on the x-y plane for a given z. [Solution diagram: 326237_solution_1.png]

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