Question

A uniform electric field exists in x-y plane. The potential of points A (-2m, 2m), B(+2m, 2m) and C(2m, 4m) are 4 V, 16V and 12 V respectively. The electric field is :

• A. $(4\hat{i}+5\hat{j})V/m$
• B. $(3\hat{i}+4\hat{j})V/m$
• C. $-(3\hat{i}+4\hat{j})V/m$
• D. $(3\hat{i}-4\hat{j})V/m$

Answer 1

The correct option is D $(3\hat{i}-4\hat{j})V/m$

Let equation of potential be $ax+by+c$ where $(x,y)$ are the co-ordinates of the point in $x,y$ plane.

so, $a\left(2\right)+b\left(2\right)+c=4$

$a(-2)+b\left(2\right)+c=16$

$a\left(2\right)+b\left(4\right)+c=12$

Solving above equations, we get $a=-3;b=4;c=2$

so equation of potential is $V=-3x+4y+2$

Now the electric field is $\overrightarrow{E}=(-dV/dx)\overrightarrow{i}+(-dV/dy)\overrightarrow{j}=3\overrightarrow{i}-4\overrightarrow{j}$