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The electric potential at any point in 3...

The electric potential at any point in 3 dimensional co-ordinate (x,y, z) space is V = `4x^2` volt. The electric field at (1m, 0m, 2m) point in `V//m` will be

A

`-8hati`

B

`8hati`

C

`-16hati`

D

`16hati`

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Knowledge Check

  • The electric potential V at any point (x, y, z) all in meters in space is given by V = 4x^(2)V . The electric field at the point (1,0,2) in V cdot m^(-1) is

    A
    8 along negative X-axis
    B
    8 along positive X-axis
    C
    16 along negative X-axis
    D
    16 along positive X-axis

  • If potential (in volts) in a region is expressed as V(x, y, z) = 6 xy- y + 2yz, the electric field (in N//C ) at point (1,1,0) is

    A
    `-(6overset^i+5overset^j+2overset^k)`
    B
    `-(2overset^i+3overset^j+overset^k)`
    C
    `-(6overset^i+9overset^j+overset^k)`
    D
    `-(3overset^i+5overset^j+3overset^k)`

  • The potential at a point x (measured in pm) due to some charges situated on the x-axis is given by V(x)=20/((x^2-4)) Volts. The electric field E at x = 4 pm is given by

    A
    `5/3V//p m` and in the `-vex` direction
    B
    `5/3V//p m` and in the `+vex` direction
    C
    `10/9V//p m ` and in the `-vex` direction
    D
    `10/9V//p m ` and in the `+vex` direction

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    The potential field depends on x and y coordinates as V=(x^2-y^2) Corresponding electric field lines in x-y plane are as

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