A conducting spherical shell has inner radius A and outer radius B. It is concen

ID: 1302153 • Letter: A

Question

A conducting spherical shell has inner radius A and outer radius B. It is concentric with

another conducting spherical shell of inner radius C and outer radius D. The inner shell has

charge +Q and the outer shell has charge -2Q. A positive charge +2Q is placed at the center

of the inner shell. Find the charge density sigma at r=A, r=B, r=C, and r=D.

b) A solid non-conducting sphere of radius R has charge spread throughout the volume so

that the charge density is where is a known constant, r is a distance from the spheres center.

Find the electric field everywhere.

when we place +2Q chrge at the center -2*Q charge induces on innerface of the ineer sphere and +3Q induces on outer surface of the inner sphere.

sigmaA = charge/area
= -2Q/(4*pi*rA^2)

sigmaB = +3Q/(4*pi*rB^2)

-3Q charge induces on inner surface of the outer sphere and +Q charge induces on outer surface of the outer sphere.

sigmaC = -3Q/(4*pi*rC^2)

sigmaD = +Q/(4*pi*rD^2)

b) let Q is the totalcharge distrubuted uniformly through out the volume.
at a point inside (r<R)
E = k*Q*r/R^3

at a point on the surface(r = R)
E = k*Q/R^2

at a point out side(r > R)
E = k*Q/r^2

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