Question

In a region of space, suppose there exists a uniform electric field $\overrightarrow{E}=10\hat{i}\text{V/m}$. If a positive charge $+1\mu \text{C}$ has been taken taken from a point $A(1,2)$ to $B(1,4)$. The work done by external force is:

• A. $+40\text{V}$
• B. $-20\text{V}$
• C. $-40\text{V}$
• D. Zero

Answer 1

The correct option is D Zero

Given:
$\overrightarrow{E}=10\hat{i}\text{V/m}$;
The electric field is uniform hence equipotential surfaces will be perpendicular to the direction of $\overrightarrow{E}$, i.e equipotential surfaces will be parallel and equally spaced $YZ-$planes.

$\Rightarrow$ Charge is taken from $A(1,2)$ to $B(1,4)$ thus its displacement is along $y-$ direction hence both the points $A\&B$ lies on the equipotential surface.
$V_A=V_B$

Therefore, from definition of electric potential

$\frac{W_{\text{ext}(A\to B)}}{q}=V_B-V_A$
$\Rightarrow W_{\text{ext}(A\to B)}=q(V_B-V_A)$

$\because V_B-V_A=0$

$\Rightarrow W_{\text{ext}}=0$

So, option $\left(d\right)$ is correct.