One of two nonconducting spherical shells of radius a carries a charge q uniformly distributed over its surface, the other carries a charge -q, also uniformly distributed. the spheres are brought together until they touch.

a.) what does the electric field look like, both outside and inside the shells?

b.) how much work is needed to move them far apart?

Explanation:

A ) The spheres are non conducting , charge will not move on the surface so neutralization of charge by + ve and - ve charge is not possible. Charges will remain intact on them . The electric field inside them will be zero . Electric field outside shell  will not be spherically symmetrical . Lines of force will emanate from the surface of positively charged shell  outwardly oriented  and end at negatively charged shell .

B )

distance between the centres of spherical shell

= 2 a

potential energy of charges

= k q₁ x q₂ / R

= k x - Q x Q / ( 2a )

= - k Q²/ 2a

So work needed to separate them to infinity will be equal to

= k Q²/ 2a