A Van de Graaff generator has a spherical metal shell as an electrode which is at a potential 15 10^6 ~V . If the dielectric strength of the surrounding medium is 5 10^7 Vm ⁻¹ , then the diameter of the shell is

Step-by-step solution

Potential difference, V=15 10^6 ~V Dielectric strength of medium =5 10^7 ~V / m Electric field intensity, E=5 10^7 ~V / m Minimum radius of spherical shell required for the purpose is given by r= V E = 15 10^6 5 10^7 =0.3 ~m Hence diameter, d=2 r=0.6 ~m =60 ~cm