Q.

The region between two concentric spheres of radii a and b(>a) contains volume charge density ρ(r)=Cr, where C is a constant and r is the radial distance as shown in figure. A point charge q is placed at the origin, r=0.

Find the value of C for which the electric field in the region between the spheres is constant (i.e. r independent).

The region between two concentric spheres of radii 'a' and 'b' ,  respectively( see figure), has volume charge density ρ = Ar , where A is a  constant and r is the

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a

C=q8πa2

b

C=q3πa2

c

C=q2πa2

d

C=q7πa2

answer is A.

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Detailed Solution

Net charge between r=a to r=r would be

Q=arρ4πr2dr=arCr4πr2dr Q=2πCr2-a2 Er=k(Q+q)r2=k2πCr2-a2+qr2

From this expression, we can see that it we put

C=q2πa2Er=kqa2= constant 

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The region between two concentric spheres of radii a and b(>a) contains volume charge density ρ(r)=Cr, where C is a constant and r is the radial distance as shown in figure. A point charge q is placed at the origin, r=0.Find the value of C for which the electric field in the region between the spheres is constant (i.e. r independent).