Question

The figure shows a set of equipotential surfaces. There are a few points marked on them. An electron is being moved from one point to other. Which of the following statements is incorrect?

• A. The electric field is directed along $+x-$ axis.
• B. Work done by the electric field, in moving the electron from $\text{B}$ to $\text{C}$, is positive.
• C. Work done by the electric field, in moving the electron from $\text{C}$ to $\text{D}$ is the same as from $\text{D}$ to $\text{E}$.
• D. As the electron moves from $\text{E}$ to $\text{A}$, the potential energy increases

Answer 1

The correct option is A The electric field is directed along $+x-$ axis.

Electric field lines are always directed from region of high potential to low potential. Besides the $\overrightarrow{E}$ is perpendicular to the equipotential surfaces.


$\Rightarrow \overrightarrow{E}$ is along $-vex-$ axis

$\therefore$ option $\left(a\right)$ is incorrect.

Electron being a $-ve$ charged particle, it will experience force in a direction opposite to $\overrightarrow{E}$. i.e. along $+vex-$ axis.

Thus, $\overrightarrow{F}$ and displacement $\left(\overrightarrow{s}\right)$ are in the same direction when electron displaced from $\text{B}$ to $\text{C}$.

$\Rightarrow W_{\text{Electric force}}\to +ve$

$\therefore \left(b\right)$ is correct.

Work done by electric force is, $W=-q(V_f-V_i)=-q\Delta V$

$\Rightarrow$ For movement of same charge $\left(e^{-}\right)$ from $\text{C}\to \text{D}$ and $\text{D}\to \text{E},\Delta V=5\text{Volt}$

$\therefore W_{C\to D}=W_{D\to E}$

Also, electron is moving against the electric field hence its P.E will increase option $\left(c\right)$ & $\left(d\right)$ are correct.


$\begin{array}{c}\text{Why this question}?\\ \text{Whenever work is done against a conservative}\\ \text{field, the associated P.E of body will increase}\\ \text{Example: on throwing a ball upwards, it is moving}\\ \text{against gravitational field. Hence, its gravitational}\\ \text{P.E}\text{increases. Similarly electrostatic P.E of}{e}^{-}\\ \text{will increase when it moves against}\overrightarrow{E}.\end{array}$