Home
Class 12
PHYSICS
A charge 2Q is distributed over three co...

A charge 2Q is distributed over three concentric non-conducting spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a , would be:

A

`(Q(a+b+c) )/(2pi epsi_0 (a^2 + b^2 + c^2) )`

B

`(Q)/(4pi epsi_0 (a + b +c) ) `

C

`(Q)/(12 pi epsi_0) (ab + bc + ca)/(abc)`

D

`(Q (a^2 + b^2 + c^2) )/(4 pi espi_0 (a^3 +b^3 + c^3) )`

Text Solution

Verified by Experts

The correct Answer is:
A

` (q_1)/(a^2) = (q_2)/(b^2) = (q_3)/(c^2) = k` (constant) ` to k (a^2 + b^2 + c^2) = 2Q`
` V(r ) = (1)/(4pi epsi_0) ((q_1)/(a) + (q_2)/(b) + (q_3)/(c ) )`
` = (1)/(4pi epsi_0) (ka + kb + kc) = (1)/(4pi epsi_0) xx ( 2Q)/((a^2 + b^2 + c^2) ) (a+b+c) `
` = (Q)/(2 pi espi_0) ((a+b+c)/(a^2+b^2+c^2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a lt b lt c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r lt a, would be :

A charge Q is uniformly distributed over the surface of two conducting concentric spheres of radii R and r (Rgtr). Then, potential at common centre of these spheres is

A charge q is distributed over two concentric hollow sphere of radii a and b(bgtc) such that the surface densities are equal.Find the potential at the common centre.is

Charges Q, 2Q , and -Q are given to three concentric conducting sphereical shells A, B and C respectively as shown in figure. The ratio of charge on the inner and outer surface of shell C will be

A conducting shell S_1 having a charge Q is surrounded by an uncharged concentric conducting spherical shell S_2 . Let the potential difference between S_1 and that S_2 be V. If the shell S_2 is now given a charge -3Q , the new potential difference between the same two shells is

A point charge +q is placed at the centre of a conducting spherical shell of inner radius a and outer radius b. Find the charge appearing on the inner and outer surface of the shell.

Figure shows three concentric thin conducting spherical shells A, B and C of radii R, 2R and 3R. The shell B is earthed A and C are given charges q and 2q respectively. Find the charges appearing on all the surface of A,B and C. [inner surface (A)0,(B)-q,(C) 4/3 q Outer surface (A) q, (B)-4/3 q,(C) 2/3 q]

A charge -Q is unformly distributed over a non-conducting semi-circular rod of radius R . The potential at the center is

There are two concentric hollow conducting spherical shells of radii r and R ( R gt r) . The charge on the outer shell is Q. What charge should be given to the inner shell, so that the potential at a point P , at a distance 2R from the common centre is zero ?

There are two concentric conducting spherical shells of radii 10 cm and 20 cm. The outer shell is charged to a potential of 50esu while inner shell is earthed. The charge on outer shell is