In a certain region of space, the potential is given by : V = k[2x^2 - y^2 + z^2]. The electric field at the point

Q: In a certain region of space, the potential is given by : $V = k[2x^2 - y^2 + z^2].$ The electric field at the point $(1, 1, 1) $ has magnitude =

b Given, $V=k\left[2 x^{2}-y^{2}+z^{2}\right]$ Electric field $, \vec{E}=-\left(\frac{d V}{d x} \hat{i}+\frac{d V}{d y} \hat{j}+\frac{d V}{d z} \hat{k}\right)$ or $, \vec{E}=-k(4 x \hat{i}-2 y \hat{j}+2 z \hat{k})$ $\operatorname{or}, \vec{E}_{(1,1,1)}=-k(4 \hat{i}-2 \hat{j}+2 \hat{k})$ Magnitude of electric field $=\left|\vec{E}_{(1,1,1)}\right|=\sqrt{k^{2}(16+4+4)}=k \sqrt{24}=2 k \sqrt{6}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

In a certain region of space, the potential is given by : $V = k[2x^2 - y^2 + z^2].$ The electric field at the point $(1, 1, 1) $ has magnitude =

A$k\sqrt 6 $
B$2k\sqrt 6 $
C$2k$$\sqrt 3 $
D$4k\sqrt 3 $

Medium

STD 11 Science
NEET
STD 12 - 2. Electric potential and capacitance
Physics

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