Three concentric metallic spherical shells radii R, 2R, 3R, are given charges Q1, Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1 : Q2 : Q3 is : (1) 1 : 2 : 3 (2) 1 : 3 : 5 (3) 1 : 4 : 9 (4) 1 : 8 : 18 Share with your friends Share 72 Somnath physics answered this Correct option: 2) By Gauss law,the surface electric field on the surface of the outermost sphere will be∮SE→.ds→=Q1+Q2+Q3εoThus total charge on the surface will be Q1+Q2+Q3Similarly, charge on the surface of the middle and inner sphere will be Q1+Q2 andQ1 respectively.But all of them has got the same charge density so,Q1+Q2+Q34π(3R)2=Q1+Q24π(2R)2=Q14πR2=>Q1+Q2+Q39=Q1+Q24=Q1=>Q1+Q24=Q1 and Q1+Q2+Q39=Q1 Q1+Q24=Q1=>Q2=3Q1 ---1.=>Q1Q2=13Q1+Q2+Q3=9Q1=>Q1+3Q1+Q3=9Q1=>Q3=5Q1 ---2.=>Q3Q1=51=>Q1:Q2:Q3=1:3:5 173 View Full Answer