Relation Between Electric Field and Electrostatic Potential

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 ______.

A capacitor having a capacitance of 100 µF is charged to a potential difference of 24 V. The charging battery is disconnected and the capacitor is connected to another battery of emf 12 V with the positive plate of the capacitor joined with the positive terminal of the battery. (a) Find the charges on the capacitor before and after the reconnection. (b) Find the charge flown through the 12 V battery. (c) Is work done by the battery or is it done on the battery? Find its magnitude. (d) Find the decrease in electrostatic field energy. (e) Find the heat developed during the flow of charge after reconnection.

Answer the following question.
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.

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.

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

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?

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

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?