Relation Between Electric Field and Electrostatic Potential

Assertion: For a non-uniformly charged thin circular ring with net charge is zero, the electric field at any point on axis of the ring is zero.

Reason: For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is zero.

How will the (i) energy stored and (ii) the electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant K?

A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 5 V. What is the potential at the centre of the sphere?

Deduce the expression for the electrostatic energy stored in a capacitor of capacitance 'C' and having charge 'Q'.

Two-point charges q₁ and q₂ are kept at a distance of r₁₂ in air. Deduce the expression for the electrostatic potential energy of this system.

The electric field in a region is given by `vec"E"` = (Ax + B) `hat"i"`, where E is in NC^-1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = -5 is V₂, then V₁ - V₂ is ______.

If an external electric field (E) is applied on the system, write the expression for the total energy of this system.

A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?