## E. field due to a hollow spherical conductor containing a point charge (NOT centred)

Imagine an uncharged spherical conductor centered at the origin
has a hole of some strange shape carved out inside it, and a charge
q is placed somewhere within this hole. What is the ﬁeld outside the
sphere?

Is it even possible to determine the electric field simply from the given information? Or is the position of the electric charge key to calculating the field?

The point charge (say it is positive) will attract all negative charge toward the inner (randomly shaped) surface of the sphere, while repelling positive charge to the outside surface of the sphere. This is clear. However, are the outer (positive) charges uniformly distributed across the sphere regardless of where the cavity's shape and position of the point charge, hence allowing the calculation of electric field outside the sphere to be considered equal to a point charge located at the center of the sphere. Or does the charge location and inner shape of the sphere affect the field outside the sphere? if yes, how? can we still calculate the charge simply by considering the actual position of the point charge to be the distance with which we calculate E=(k(q1)(q2))/(r^2)?

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 Is this like a cavity that is not connected to the open air outside like a tunnel. If its not then you would just use Gauss's law and the charge enclosed to find the E field.

 Tags conductor, electrcity, electric field, gauss's law, point charge