Past exam of the physics 2 paper of the University of Oxford / 2013 / 1

Newton's second law applies separately to each body's total force: zero force on $q_1$ means zero acceleration of $q_1$, while a nonzero force on a free $q_2$ gives nonzero acceleration of $q_2$. It does not assert that those two forces must be equal and opposite.

The conducting shell is a third interacting body. Its induced surface charges shield the cavity from the external charge, while charges on its outer surface can still exert a force on $q_2$. Reaction forces act on the shell and, if it is held fixed, on its supports. In the electrostatic limit the force balance of the complete isolated charge–shell system is ${\mathbf{F}}_1+{\mathbf{F}}_2+{\mathbf{F}}_{\mathrm{shell}}=0$. Thus the given situation is consistent with both Newton's second law and Newton's third law once the shell is included.

Shielding removes the cavity field due to external charges; it does not generally remove the force of the inner surface charges induced by an off-centre $q_1$. Zero total force on $q_1$ is an additional condition, satisfied for example when it is at the centre of a spherical cavity.