Question

Does the unconnected conductor affect the E-field and the equipotential pattern? why?

Answer 1

Yes , the unconnected conductor affect the electric field and the equipotential pattern

Conductors contain free charges that move easily. When excess charge is placed on a conductor or the conductor is put into a static electric field, charges in the conductor quickly respond to reach a steady state called electrostatic equilibrium.

A conductor placed in an electric field will be polarized, the result of placing a neutral conductor in an originally uniform electric field . The field becomes strong near the conductor but entirely disappears inside it.

A spherical conductor in static equilibrium with an originally uniform electric field. Free charges move within conductor, polarizing it, until electric field lines are perpendicular to the surface. The electric field lines end on excess negative charge on one section of the surface and began again on excess positive charge on the opposite side. No electric field exists inside conductor, since free charges in the conductor would continue having in response to any field until it was neutralised.