Question

Determine the electric field if potential of this field depends on x, y co-ordinates as V = 10 axy–

• A. 10a (y$\widehat{i}$ + x$\widehat{j}$)
• B. –10a (y$\widehat{i}$ + x$\widehat{j}$)
• C. –a (y$\widehat{i}$ + x$\widehat{j}$)
• D. –10a (x$\widehat{i}$ + y$\widehat{k}$)

Answer 1

Answer: (B)

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

Answer 2

E_x = – $\frac { \partial V } { \partial \mathrm { x } }$ $\hat { \mathbf { i } }$ = – (10axy) = – 10ay $\hat { \mathbf { i } }$

E_y = $\frac { - \partial \mathrm { V } } { \partial \mathrm { y } }$ = – (10axy) $\hat { \mathbf { i } }$ = – 10ax $\hat { \mathrm { j } }$

E = – 10a (y + x)