Question

Describe schematically the equipotential surfaces corresponding to:
i) a constant electric field in the z direction.
ii) a field that uniformly increases in magnitude but remains in a constant (say, z) direction.
iii) a single positive charge at the origin
iv) a uniform grid consisting of long equally spaced parallel charged wires in a plane.

Answer 1

i) For constant electric field in the z direction:
Constant electric field can be represented by parallel field lines, so the surface perpendicular to these field lines is a plane.
Hence, the equipotential surfaces for a constant electric field in the $z\text{direction}$ are plane parallel to the $xy-\text{plane}$ and the equipotential surfaces are equidistant from each other.


ii) As, the magnitude of electric field increases uniformly, and direction remains constant i.e., $z$-direction.so, potential difference also increases. This electric field can be represented by straight lines along the $z$-direction. The plane normal to the $z$-axis will be equipotential surfaces. To increase the potential difference between two surfaces, distance between the surfaces will decrease, therefore, equipotential surfaces will not be equidistant.



iii) For a single positive charge, electric field lines produced by charge moves radially outwards.
The surface perpendicular to the field lines will form a sphere. Therefore, equipotential surfaces for a single positive charge are concentric spheres with the charge at the centre.


iv) If a uniform grid consisting of long equally spaced parallel charged wires is in a plane, then the equipotential surface will be a periodically varying shape near the given grid and this varying shape will gradually reach the shape of planes parallel to the grid at a larger distance.