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

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 hati+x hatj) (B) -10 a[y hati+x hatj] (C) -a[y hati+x hatj] (D) -10 a[x hati+y hatk]

Tardigrade Admin · Accepted Answer

V=10 axy Ex=(-d V/d x)=-10 a y, Ey=(-d V/d y)=-10 a x vecE=-10 a(y hati+x hatj)

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

$10 a (y \hat{i} + x \hat{j})$

$- 10 a [y \hat{i} + x \hat{j}]$

$- a [y \hat{i} + x \hat{j}]$

$- 10 a [x \hat{i} + y \hat{k}]$

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

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

10a(yi^+xj^​)

−10a[yi^+xj^​]

−a[yi^+xj^​]

−10a[xi^+yk^]