# An electric potential is V ( x , y ) = A s i n ( k x ) c o s ( k y ) Where A and k are...

## Question:

An electric potential is

{eq}V(x,y)=Asin(kx)cos(ky) {/eq}

Where A and k are constants. What is the y component of the electric field?

## Electric potential:

Electric potential is defined as the energy or work needed to move a charge from its initial position to a specified position.

Given data:

Electric potential {eq}V\left( {x,y} \right) = A\sin \left( {kx} \right)\cos \left( {ky} \right) {/eq}

The expression for electric field is given by,

{eq}\begin{align*} \vec E &= - \Delta \vec V\\ \vec E &= - \left[ {\dfrac{{\partial V}}{{\partial x}}\hat i + \dfrac{{\partial V}}{{\partial x}}\hat j + \dfrac{{\partial V}}{{\partial x}}\hat k} \right] \end{align*} {/eq}

Substitute the values in above expression,

{eq}\vec E = - Ak\cos \left( {kx} \right)\cos \left( {ky} \right)\hat i + kA\sin \left( {kx} \right)\sin \left( {ky} \right)\hat j + 0 {/eq}

Thus the {eq}Y {/eq} component of the given electric field is {eq}{\vec E_y} = kA\sin \left( {kx} \right)\sin \left( {ky} \right) {/eq}.