Question

The most appropriate relationship between electric field and electric potential can be described as
($C$ is an arbitrary path connecting the point with zero potential infinity)

• A. $V_E=-{\int }_{C}E.dl$
• B. $E_V=-{\int }_{C}V.dl$
• C. $V_E=-\int E.dl$
• D. $E_V=-\int E.dl$

Answer 1

The correct option is A $V_E=-{\int }_{C}E.dl$

Let $\Delta V=V_B-V_A$ be the electrostatic potential energy difference between any two points A and B in the electric field. The electric potential difference between points A and B is given by:

$\Delta V=V_B-V_A=\frac{\Delta V}{q_0}=\frac{V_B-V_A}{q_0}$

$\Delta V=V_B-V_A=-q_0{\int }_A^B\overrightarrow{E}.\overrightarrow{dl}$

$\Delta V=\frac{\Delta V}{q_0}=-{\int }_A^B\overrightarrow{E}.\overrightarrow{dl}$ ...(i)

If C is an arbitrary path connecting the point with zero potential at infinity. Then, equation (i) becomes:

$V=-{\int }_{C}E.dl$