Home
Class 12
PHYSICS
Charge is distributed within a sphere of...

Charge is distributed within a sphere of radius R with a volume charge density `p(r)=(A)/(r^(2))e^(-2r//a),` where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

A

`a/2 log (1 - Q/(2pi a A))`

B

`a/2 log(1/(1- Q/(2pi a A))`

C

`a log (1 - Q/(2pi a A))`

D

`a log(1/(1- Q/(2pi a A)))`

Text Solution

Verified by Experts

The correct Answer is:
B
`Q = int_(0)^R rho 4 pi r^2 dr`
`=int_(0)^(R ) A/(r^2) e^(-(2r)/(a)) 4 pi r^2 dr = 4 pi A int_(0)^(k) e^(-2r//a) dr = (4 pi A)/((-2//a)) [e^(-2r//a)]_(0)^(R )`
`Q = -2 pi A a(e^(-(2R)/a - 1))`
`Q = - 2pi A a e^(-(2R)/a) + 2 pi a A`
`implies e^(-2R//a) = (2 pi a A -Q)/(2 pi a A) implies R = a/2 log(1/(1 - Q/(2pi a A)))`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A conducting sphere of radius r has a charge . Then .

A solid sphere of radius R is charged with volume charge density p=Kr^(n) , where K and n are constants and r is the distance from its centre. If electric field inside the sphere at distance r is proportional to r^(4) ,then find the value of n.

A solid sphere of radius R has a charge Q distributed in its volume with a charge density rho=kr^a , where k and a are constants and r is the distance from its centre. If the electric field at r=(R)/(2) is 1/8 times that r=R , find the value of a.

A sphere of radius R_(0 carries a volume charge density proportional to the distance (x) from the origin, rho=alpha x where alpha is a positive constant.The total charge in the sphere of radius R_(0) is

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by , rho(r)=kr , where r is the distance from the centre. Two charge A and B, of –Q each, are placed on diametrically opposite points, at equal distance, a from the centre. If A and B do not experience any force, then:

A sphere of radius R contains charge density rho(r )=A (R-r ) , for 0 lt r lt R . The total electric charge inside the sphere is Q. The electric field inside the sphere is

A sphere of radius R contains charge density rho(r )=A (R-r ) , for 0 lt r lt R . The total electric charge inside the sphere is Q. The electric outside the sphere is (k=1/(4pi in_(0)))

A charge +Q , is uniformaly distributed within a sphere of radius R. Find the electric field, due to this charge distribution, at a point distant r form the centre of the spehre where : (i) 0 lt r lt R and (ii) r gt R