Determine the electric field strength vector | vedclass

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(B) The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -
abla V$.Given $V = 10axy$.The components of th

Vedclass · Accepted Answer

$-10a(y \hat{i} + x \hat{j})$

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(B) The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -
abla V$.Given $V = 10axy$.The components of the electric field are given by:$E_x = -\frac{\partial V}{\partial x} = -\frac{\partial}{\partial x}(10axy) = -10ay$$E_y = -\frac{\partial V}{\partial y} = -\frac{\partial}{\partial y}(10axy) = -10ax$$E_z = -\frac{\partial V}{\partial z} = 0$Thus,the electric field vector is $\vec{E} = E_x \hat{i} + E_y \hat{j} + E_z \hat{k} = -10ay \hat{i} - 10ax \hat{j} = -10a(y \hat{i} + x \hat{j})$.

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V = 10axy$.

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