A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of rad

Question

A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q.

If the spheres were joined by a conducting wire, what would the electric field and the potential be at a distance r from the center of the inner sphere (R<r<3R)?

A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q. If the spheres were joined by a conducting wire, what would the electric field and the potential be at a distance r from the center of the inner sphere (R

Explanation / Answer

when they are connected charge separation takes place until they attain same potantail.
let q1 and q2 are the final charges on inner and outer spheres.

q1 + q2 = 2*Q - Q

q1 + q2 = Q --(1)


finally

V1(inner sphere) = V2(outer sphere)

k*q1/R = k*q2/(3*R)

q1 = q2/3

3*q1 = q2

3*q1 = (Q-q1)

4*q1 = Q

q1 = Q/4 (charge on ineer sphere)


at R < r < 3*R

here we consider only charge on inner sphere. because charge on outer sphere does not contribute to electric fileld.

E = k*q1/r^2

E = k*Q/(4*r^2)

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