The question was something like this -> If I have a charge kept inside a cavity made in a sphere of radius $R$ and the radius of the cavity is $r $ where $(r<R)$. Now I do not keep the charge $q$ inside the cavity symmetrically instead I keep it at some distance away from the center of the cavity and hence the sphere. Then I know that in order to make the inner surface equipotential there will more negative charge on the side of the cavity closer to the charge $q$ and lesser on the far side. But in his lectures, Walter Lewin then claims that the charge distribution on the outer surface will be uniform in order to make it equipotential but I don't understand, since the field lines can just hit perpendicular to make it equipotential then why is it necessary to have asymmetric surface charge distribution.
Any and all help will be appreciated. My question once again, is the charge distribution on the outer surface symmetric or not, if so why?