Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 1

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In figure electric field formula is shown.

Electric Field Formula

In figure electric field formula is shown.

Q: 1. Two charges and are located apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Answer:

There are two charges,

Distance between the two charges,

Consider a point P on the line joining the two charges, as shown in the given figure

Q 1 Distance of the Two Charges

Q 1 Distance of the Two Charges

Q 1 Distance of the Two Charges

Distance of point P from charges

Let the electric potential (V) at point P be zero.

Potential at point P is the sum of potentials caused by charges respectively.

Where,

Permittivity of free space

For , equation (i) reduces to

The System of Two Charges at a Distance from the Negative Charge

Therefore, the potential is zero at a distance of 10 cm from the positive charge between the charges.

Suppose point P is outside the system of two charges at a distance s from the negative charge, where potential is zero, as shown in the following figure

Q 1 1 The System of Two Charges at a Distance s from the Negative Charge

Q 1 1 Two Charges at a Distance from the Negative Charge

Q 1 1 The System of Two Charges at a Distance s from the Negative Charge

For this arrangement, potential is given by,

For

Therefore, the potential is zero at a distance of from the positive charge outside the system of charges.

Q: 2. A regular hexagon of side has a charge at each of its vertices. Calculate the potential at the centre of the hexagon.

Answer:

The given figure shows six equal amount of charges, q, at the vertices of a regular hexagon.

Ch 2 Centre of the hexagon

Ch 2 Centre of the Hexagon

Ch 2 Centre of the hexagon

Where,

Charge,

Side of the hexagon,

Distance of each vertex from centre

Electric potential at point O,

Where,

Permittivity of free space

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