If the electric potential is given by V = 4x | vedclass

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Question

(B) The electric field $\vec{E}$ is related to the potential $V$ by the relation $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x} \hat{i}

Vedclass · Accepted Answer

$5$

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(B) The electric field $\vec{E}$ is related to the potential $V$ by the relation $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} ight)$.Given $V = 4x + 3y$.The $x$-component of the electric field is $E_x = -\frac{\partial V}{\partial x} = -\frac{\partial}{\partial x}(4x + 3y) = -4 \, 	ext{V/m}$.The $y$-component of the electric field is $E_y = -\frac{\partial V}{\partial y} = -\frac{\partial}{\partial y}(4x + 3y) = -3 \, 	ext{V/m}$.The magnitude of the electric field is $E = \sqrt{E_x^2 + E_y^2}$.Substituting the values,$E = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \, 	ext{V/m}$ (or $	ext{N/C}$).

If the electric potential is given by $V = 4x + 3y$,what is the electric field at the point $(2, 1)$?

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