At what distance 'd' from the surface of asolid sphere of radius 'R', (a)potential is sme as at a distance (R)/(2) from the centre ? (b) field strengt is ame as at a distance (R)/(4) fromcentre.

At what distance 'd' from the surface of asolid sphere of radius 'R',

1.	At what distance 'd' from the surface of asolid sphere of radius 'R', (a)potential is sme as at a distance (R)/(2) from the centre ? (b) field strengt is ame as at a distance (R)/(4) fromcentre.
Answer» Solution :(a) Given, `V_("outside") = V_("inside")` No Such POINT will EXIST. Because potential at CENTRE is `(-1.5GM)/(R)`. Potential at surface is `(-GM)/(R)` and potential at infinity is zero . From centre to surface potential between `(-1.5GM)/(R)` and `(-GM)/(R)`. From surface to infinity potential varies between `(-GM)/(R)` and zero . Given, `E_("inside") = E_("outside")` `:. (GM)/(R^(3))(r_1) = (GM)/(r_(2)^(2))` Here, `r_(1)` and `r_(2)` are the distances from centre. `:. (GM)/(R^(3)) ((R)/(4)) = (GM)/((R+d)^(2))` Solving this EQUATION , WE get `d=R`.