Question

In a region, the potential is represented by $V(x,y,z)=6x-8xy-8y+6yz$, where V is in volts and x, y, z are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1, 1,1) is :

• A. $6\sqrt{5}N$
• B. $30N$
• C. $24N$
• D. $4\sqrt{35}N$

Answer 1

The correct option is D $4\sqrt{35}N$

$V_{(x,y,z)}=6x-8xy-8y+6yz$

$E_x=-\frac{\partial V}{\partial x}=-6+8y$

$E_y=-\frac{\partial V}{\partial y}=8x+8-6z$

$E_z=-\frac{\partial V}{\partial z}=-6y$

$\overrightarrow{E}=(-6+8y)\hat{i}+(8x+8-6z)\hat{j}-6y\hat{k}$

${\overrightarrow{E}}_{(1,1,1)}=2\hat{i}+10\hat{j}-6\hat{k}$

$|\overrightarrow{E}|=2\sqrt{35}N{C}^{-1}$

$F=qE=2\times 2\sqrt{35}=4\sqrt{35}N$