Electric potential and electric potential energy

In a region of constant potential

Four equal point charge Q are to be placed at the corner of square ABCD of side 1 m one at a time. Find the energy in the system after each charge is positioned

where  

Electric potential at any point x, y, z in the space is given . Find the force experienced by a charge particle q at point (1, 1, 1)

 Consider a uniform electric field in the z-direction. The potential is a constant

Electric potential at any point x, y, z in the space is given . Find the electric field at any point (x, y, z)

How much work is required to bring together the three given charges from infinity to the corners of an equilateral triangle of side length 1 cm? 

 The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is W. Then the potential at that point is

A spherical shell of radius R is carries a uniform surface charge q. Take the reference point at ∞. Find the potential at r<R .

A spherical shell of radius R is carries a uniform surface charge q. Take the reference point at ∞. Find the potential at r>R

A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will

The work done is carrying a charge q once round a circle of radius r with a charge Q at the centre is

Two positive point charges of 12 and 8 microcoulombs respectively are placed 10 cm apart in air.

The work done to bring them 4 cm closer is

A point charge q is located at P (2, 3, 3) in xyz coordinate. Find the potential differences between A and B
A = (2, 2, 3)
B = (-2, 3, 3)

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

Four point charges + q, + q,- q and - q are placed respectively at the comers A,B,C and D of a square of side a. The electric potential at the centre O of the square is