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

$(a)\;(4 \hat{i}+5 \hat{j})\qquad(b)\;(3 \hat{i}+4 \hat{j})\qquad(c)\;-(3 \hat{i}+4 \hat{j})\qquad(d)\;(4 \hat{i}-5 \hat{j})$

Answer : (d) $\;(4 \hat{i}-5 \hat{j})$
Explanation :
Let the electric field be $\;a \hat{i} +b \hat{j}$
Then
$V_{A}-V_{B}=- [(a \hat{i}+b \hat{j})\;.(4 \hat{i})]=-4a=-12$
$a=3$
$V_{A}-V_{C}=- [(a \hat{i}+b \hat{j})\;.(-2 \hat{j})]=2b$
$2b=-8$
$b-4$
$\overrightarrow{E}=3 \hat{i} -4 \hat{j}$ .