Question

Determine the electric field strength vector if the potential of the field depends on x, y coordinates as $V=a(x^2-y^2)$, where a is a constant.

• A. $\overrightarrow{E}=-2a(x\hat{i}-y\hat{j})$
• B. $\overrightarrow{E}=-a(x\hat{i}-y\hat{j})$
• C. $\overrightarrow{E}=-\frac{a(x\hat{i}-y\hat{j})}{2}$
  
• D. $\overrightarrow{E}=-\frac{a(x\hat{i}-y\hat{j})}{4}$

Answer 1

The correct option is A $\overrightarrow{E}=-2a(x\hat{i}-y\hat{j})$

$\overrightarrow{E}=-▽V$ ( negative of gradient of V)

$\overrightarrow{E}=-(\frac{dV}{dx}\hat{i}+\frac{dV}{dy}\hat{j})=-a(2x\hat{i}+2y\hat{j})$