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The potential at any point is given by V...

The potential at any point is given by `V = x(y^2 - 4 x^2)`. Calculate the cartesian components of the electric field at the point.

Text Solution

Verified by Experts

Here `V = x(y^2 - 4 x^2)`. So
`E_x = -(del V)/(del x) = -(del)/(del x) [xy^2 - 4x^3]`
=`- [y^2 - 12x^2]`
or `E_x = [12 x ^2 - y^2]`
Similarly,
`E_y = -(del V)/(del y) = -(del)/(del y) [x (y^2 - 4 x^2)]`
or =`- (del)/(del y) [xy^2 - 4 x^3] = -2x y`
`E_z = -0` because V does not depend upon the z- coordinate.
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