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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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Knowledge Check

  • 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)`

  • The electirc potential at a point (x, y, z) is given by V = -x^(2)y - xz^(3) + 4 The electric field vecE at that point is

    A
    `vecE = hati (2xy +z^(3)) + hatj x^(2) + hatk 3xz^(2)`
    B
    `vecE = hati 2xy + hatj (x^(2) + y^(2)) + hatk (3xz - y^(2))`
    C
    `vecE = hati z^(3) + hatj xyz + hatk z^(2)`
    D
    `vecE = hati (2xy - z^(3)) + hatj xy^(2) + hatk 3z^(2) x`

  • The electric potential at a point (x, y, z) is given by V= -x^(2)y -xz^(3)+4 The electric field vec(E ) at that point is

    A
    `vec(E )= hat(i) 2xy + hat(j) (x^(2) + y^(2)) + hat(k) (2xy- y^(2))`
    B
    `vec(E )= hat(i) z^(3) + hat(j) xyz + hat(k) z^(2)`
    C
    `vec(E )= hat(i) (2xy+ z^(3)) + hat(j) xy^(2) + hat(k) 3z^(2)x`
    D
    `vec(E )= hat(i) (2xy + z^(3)) + hat(j) x^(2) + hat(k) 3xz^(2)`

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