For the situation shown in (fig. 3.147), mark the correct statement (s).

Options

A. Potential of the conductor is `q//4piepsilon_0(d+R)`
B. Potential of the conductor is `q//4piepsilon_0d`
C. Potential of the conductor cannot be determined as nature of distribution of induced charges is not known.
D. Potential at point B due to induced charges is `-qR//4piepsilon_0(d+R)d`

Answer

A, D

Explanation

a.,d.
As no charge is present inside the conductor potential at any point inside the conductor is same as that of the potential or conductor. So, potential of the conductor `=` potential at the center `=V_(q)=V_("induced charges")`
`V_("conductor")=(q)/(4piepsilon_(0)(d+R))+0`
As the total induced charge at conductor's surface is equal zero and hence to the potential at center due to the inductor charge. For point `B`,
`V_("conductor")=V_("at point"B)=V_(q)+V_("induced charges")`
or `V_("induced charges")=(q)/(4piepsilon_(0)(d+R))-(q)/(4piepsilon_(0)d)`
`=(-qR)/(4piepsilon_(0)d(d+R)`