Question

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V=10\, axy$

• A. $10 a(y \hat{i}+x \hat{j})$
• B. $-10 a[y \hat{i}+x \hat{j}]$
• C. $-a[y \hat{i}+x \hat{j}]$
• D. $-10 a[x \hat{i}+y \hat{k}]$

Answer 1

Answer: (B)

$V=10 \, axy$
$E_{x}=\frac{-d V}{d x}=-10 \,a y, $
$E_{y}=\frac{-d V}{d y}=-10 \,a x$
$\vec{E}=-10 a(y \hat{i}+x \hat{j})$