# Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 5

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Q: 12. A charge of is located at the origin. Calculate the work done in taking a small charge of from a point to a point , via a point .

Answer:

Charge located at the origin,

Magnitude of a small charge, which is taken from a point P to point R to point

All the points are represented in the given figure.

Point P is at a distance,, from the origin along z-axis.

Point Q is at a distance,, from the origin along y-axis

Potential at point P,

Potential at point P,

Work done (W) by the electrostatic force is independent of the path.

Where,

Therefore, work done during the process is .

Q: 13. A cube of side has a charge at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

Answer:

Length of the side of a cube

Charge at each of its vertices

A cube of side b is shown in the following figure.

is the distance between the centre of the cube and one of the eight vertices

Therefore, the potential at the centre of the cube is .

The electric field at the centre of the cube, due to the eight charges, gets cancelled. This is because the charges are distributed symmetrically with respect to the centre of the cube. Hence, the electric field is zero at the centre.