The electric potential at a point (x, y) in t | vedclass

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(B) The electric field components are given by the negative gradient of the potential:$E_x = -\frac{\partial V}{\partial x} = -\frac{\partial}{\partia

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$r$

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(B) The electric field components are given by the negative gradient of the potential:$E_x = -\frac{\partial V}{\partial x} = -\frac{\partial}{\partial x}(-kxy) = ky$$E_y = -\frac{\partial V}{\partial y} = -\frac{\partial}{\partial y}(-kxy) = kx$The magnitude of the electric field intensity $E$ is given by:$E = \sqrt{E_x^2 + E_y^2} = \sqrt{(ky)^2 + (kx)^2}$$E = k\sqrt{x^2 + y^2}$Since the distance from the origin is $r = \sqrt{x^2 + y^2}$,we have:$E = kr$Therefore,the field intensity varies directly with the distance $r$ from the origin,i.e.,$E \propto r$.

The electric potential at a point $(x, y)$ in the $x-y$ plane is given by $V = -kxy$. The field intensity at a distance $r$ from the origin varies as

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