Question

Question: A conducting sphere is placed between two charged parallel plates such as those shown in Figure. Does the electric field inside the sphere depend on precisely where between the plates the sphere is placed? What about the electric potential inside the sphere? Do the answers to these questions depend on whether or not there is a net charge on the sphere? Explain your reasoning.

Short answer

Answer

The electric field inside the sphere does not depend on precisely where between the plates the sphere is placed. Electric potential inside the sphere is never changed. No, the net charge is not required to answer the question.

Step-by-step solution

Definition of electric potential

The term electric potential is defined as the amount of work done by the unit charge in moving from one point to another against electric field.

The electric field obtained by the relation$\overrightarrow{\mathbf{E}}\mathbf{=}\mathbf{-}\overrightarrow{\mathbf{~}}\mathbf{NV}$ taking both sides line integral

$$\begin{gathered} \oint \overrightarrow{E}.d\overrightarrow{l}=\oint -\overrightarrow{\nabla }V· \\ \oint \overrightarrow{E}.d\overrightarrow{l}=0 \end{gathered}$$

Explain the answer for the questions

Conclude that work done is not depend on path and is zero for closed path. And no, the electric field inside the sphere depend on precisely where between the plates the sphere is placed.

$$\begin{gathered} V=\int Edr \\ =0dr \\ =c \end{gathered}$$

Due to above expression conclude that electric potential is constant and equal to zero moreover is not depend upon the net charge on the sphere.

Hence, the electric field inside the sphere does not depend on precisely where between the plates the sphere is placed. Electric potential inside the sphere is never changed. No, the net charge is not required to answer the question.