First slide

Electrostatic potential

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 metres. The electric force experienced by a charge of2 coulomb situated at point ( 1, 1, 1) is :

Moderate

A

$6 \sqrt{5} N$
B

30 N
C

24 N
D

$2 \sqrt{35} N$

Solution

$\vec{E} = \frac{\partial V}{\partial x} \hat{i} - \frac{\partial V}{\partial y} \hat{j} - \frac{\partial V}{\partial z} \hat{k}$
$= - [(6 - 8 y) \hat{i} + (- 8 x - 8 + 6 z) \hat{j} + (6 y) \hat{k}]$
At(1, 1, 1); $\vec{E} = 2 \hat{i} + 10 \hat{j} - 6 \hat{k}$
$\Rightarrow \vec{E} = \sqrt{2^{2} + 10^{2} + 6^{2}} = \sqrt{140} = 2 \sqrt{35}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App