If potential (in volts) in a region is expressed as the electric field (in N/C) at point (1, 1, 0) is [2015]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
If potential (in volts) in a region is expressed as $V (x, y, z) = 6 x y - y + 2 y z,$ the electric field (in N/C) at point (1, 1, 0) is [2015]

1 $- (2 \hat{i} + 3 \hat{j} + \hat{k})$

2 $- (6 \hat{i} + 9 \hat{j} + \hat{k})$

3 $- (3 \hat{i} + 5 \hat{j} + 3 \hat{k})$

4 $- (6 \hat{i} + 5 \hat{j} + 2 \hat{k})$

Ans.
(4)

The electric field $\vec{E}$ and potential V in a region are related as $\vec{E} = - [\frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k}]$

Here, $V (x, y, z) = 6 x y - y + 2 y z$

$∴ \vec{E} = - [\frac{\partial}{\partial x} (6 x y - y + 2 y z) \hat{i} + \frac{\partial}{\partial y} (6 x y - y + 2 y z) \hat{j} + \frac{\partial}{\partial z} (6 x y - y + 2 y z) \hat{k}]$

$= - [(6 y) \hat{i} + (6 x - 1 + 2 z) \hat{j} + (2 y) \hat{k}]$

At point (1, 1, 0),

$\vec{E} = - [(6 (1)) \hat{i} + (6 (1) - 1 + 2 (0)) \hat{j} + (2 (1)) \hat{k}] = - (6 \hat{i} + 5 \hat{j} + 2 \hat{k})$

Want Us to Email you About Special Offers & Updates?