A large metal sphere has five times the diameter of a smallersphere and carries

Question

A large metal sphere has five times the diameter of a smallersphere and carries three times as much charge. Both spheres areisolated, so their surface charge densities are uniform. (a) Express the potential of the large sphere in terms of thepotential Vs of the small sphere.
(b) Express the electric field strength at the surface of thelarge sphere in terms of that of the small sphere,Bs.
A large metal sphere has five times the diameter of a smallersphere and carries three times as much charge. Both spheres areisolated, so their surface charge densities are uniform. (b) Express the electric field strength at the surface of thelarge sphere in terms of that of the small sphere,Bs.

Explanation / Answer

We have potential on the surface of charged sphere V =kq/R therefore Vlarge/Vsmall = (qlarge/qsmall)(Rsmall/Rlarge)                                         =(3)/(5) Therefore Vlarge=(3/5)Vsmall Now we have electric field strength on the surface os tehchsrged sphere is E = kq/R2 therefore Elarge/Esmall = (qlarge/qsmall)(Rsmall/Rlarge)2                                         =(3)/(25) Therefore Elarge=(3/25)Esmall therefore Elarge/Esmall = (qlarge/qsmall)(Rsmall/Rlarge)2                                         =(3)/(25) Therefore Elarge=(3/25)Esmall therefore Elarge/Esmall = (qlarge/qsmall)(Rsmall/Rlarge)2                                         =(3)/(25) Therefore Elarge=(3/25)Esmall

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