Three concentric spherical metallic shells X , Y and Z of radius a , b and c respectively a < b < c have surface charge densities σ , – σ and σ , respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm , respectively. The radius of shell Z is _____ cm .

Step-by-step solution

The charges on the spheres are q X = σ 4 π a 2 q Y = - σ 4 π b 2 q Z = σ 4 π c 2   It is given that V X = V Z So, q X 4 π ε 0 a + q Y 4 π ε 0 b + q Z 4 π ε 0 c = q X 4 π ε 0 c + q Y 4 π ε 0 c + q Z 4 π ε 0 c ⇒ σ 4 π a 2 a - σ 4 π b 2 b + σ 4 π c 2 c = σ 4 π ( a 2 - b 2 + c 2 ) c ⇒ c ( a - b + c ) = ( a 2 - b 2 + c 2 ) ⇒ c = a + b = 2   cm + 3   cm = 5 &#1