Two metal spheres, one of radius R and the other of radius 2 R respectively have the same surface charge density . They are brought in contact and separated. What will be the new surface charge densities on them?

Step-by-step solution

The surface charge density of a closed surface area having charge Q is given by = Charge Area = Q A or Q = A Thus, the charges on sphere P and Q having same charge density as shown in the figure below is given by gathered Q _ P = 4 R ^2=4 R ^2 and Q _ Q = 4 (2 R )^2=16 R ^2 gathered when they are brought in contact with each other, the total charge will be aligned Q _ t & = Q _ P + Q _ Q = & 4 R ^2+16 R ^2 [From Eq. (i) and (ii)] & =20 R ^2 aligned In connection of two charged conducting bodies, the potential will