Question

draw the equipotential surface for an electric field pointing in +z direction with its magnitude increasing at constant rate along -z direction.​

Answer 1

Answer :

$\star$ If potential of a surface (imaginary or physically existing) is same throughout then such surface is known as an equipotential surface.

Properties of equipotential surfaces :

• When a charge is shifted from one point to another point on an equipotential surface then work done against electrostatic force is zero.
• Electric field is always perpendicular to equipotential surfaces.
• Two equipotential surfaces don't cross each other.

Diagram : Refer to the attached image!

Additional Information :

• Electric potential is a characteristic of an electric field it doesn't matter a charged object is placed in that field or not.
• It is measured in J/C or volt.

Answer 2

Answer:

Explanation:

Since dx is small, E is assumed uniform along BA.

Let the force acting on a unit positive charge at A = |E |

∴ Work done in moving the  unit positive charge from A to B against the electric field, dw = - E x dx

Since, dw = dv ( potential difference between A and B)

∴ dv = -E x dx

or E = - dv/dx

Thus, electric field at a point is equal to the negative of the potential gradient at that point.