Question

Electric potential in a region is given by $V=6x-8xy^{2}-8y+6yz-4z^{2}$ The magnitude of electric force acting on a $2C$ charge placed at origin is (where $x,y$ and $z$ are in meter and $V$ is in volt)

• A. $2N$
• B. $20N$
• C. $6N$
• D. $8N$

Answer 1

Answer: (B)

$\overset{ \rightarrow }{E}_{x}=-\frac{d V}{d x}=-\left[6 - 8 y^{2}\right]\hat{i}$
$\overset{ \rightarrow }{E}_{y}=-\frac{d V}{d y}=-\left[\right.-16xy-8+6z\left]\right.\hat{j}$
$\overset{ \rightarrow }{E}_{z}=-\frac{d V}{d y}=-\left[\right.6y-8z\left]\right.\hat{k}$
at origin $\overset{ \rightarrow }{E}=-6\hat{i}+8\hat{j}+0\hat{k}$
$\left|\right.\overset{ \rightarrow }{E}\left|\right.=10\frac{N}{C}$
$F=qE=20N$