# Physics Class 12 NCERT Solutions: Chapter 21 Electrostatic Potential and Capacitance Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 20. Two charged conducting spheres of radii and are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

Let be the radius of a sphere A, be the charge on the sphere, and be the capacitance of the sphere. Let b be the radius of a sphere B, be the charge on the sphere, and be the capacitance of the sphere. Since the two spheres are connected with a wire, their potential (V) will become equal.

Let EA be the electric field of sphere A and EB be the electric field of sphere B. Therefore, their ratio,

However,

And,

Putting the value of (2) in (1) , we obtain

Putting the value of (2) in (1) , we obtain

Therefore, the ratio of electric fields at the surface is .

Q: 21. Two charges are located at points respectively.

(A) What is the electrostatic potential at the points?

(B) Obtain the dependence of potential on the distance r of a point from the origin when .

(C) How much work is done in moving a small test charge from the point to along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

(A) Zero at both the points

Charge is located at and charge is located at . Hence, they form a dipole. Point is on the axis of this dipole and point (x, y, 0) is normal to the axis of the dipole. Hence, electrostatic potential at point is zero. Electrostatic potential at point is given by,

Where,

Permittivity of free space

Dipole moment of the system of two charges

(B) Distance r is much greater than half of the distance between the two charges. Hence, the potential (V) at a distance r is inversely proportional to square of the distance

i.e.. ,

(C) Zero

The answer does not change if the path of the test is not along the x-axis.

A test charge is moved from point to point along the x-axis. Electrostatic potential at point is given by,

Electrostatic potential, , at point is given by,

Hence, no work is done in moving a small test charge from point to point along the x-axis.

The answer does not change because work done by the electrostatic field in moving a test charge between the two points is independent of the path connecting the two points.

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