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In a certain region of space , the poten...

In a certain region of space , the potential is given by : ` V = K [2 x^2 -y^2 - y^2 z^2 ]`. The electric field at the point (1.1.1) has magnitude =.

A

` k sqrt 6 `

B

` 2 k sqrt 6`

C

` 2 k sqrt 3`

D

` 4 k sqrt 3`

Text Solution

Verified by Experts

The correct Answer is:
B
` V = K ( 2 x^2 - y ^2 + Z^2 )` ltbRgt ` E_x=- (dV) /(dx) =- 4 xK`, `E_y =- (dV)/(dY) = + 2Y`
` E_2 =- (dV) /(dz) =- 2K_2`
`cex E=- 4 x k hat I + 2 y K hat j - 2 k2 hat k`
` vec E_(1,1,1) =- 4 k + 2 hat I - 2 k hat k`
` E= k sqrt ((-4)^2 + (2)^2 + (-2)^2 ) = 2k sqrt 6`.
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