The electric potential at a point is space is given by the relation V = 23x - 27y + 11y² + 72.What is the magnitude of the electric field (in V/m)at the point r = (3.0,2.0,1.0)?

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29The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -\nabla V$, where $\nabla V$ represents the gradient of the potential. Given $V = 23x - 27y + 11y^2 + 72$, we can calculate the components of the electric field as follows:- $E_x = -\frac{\partial V}{\partial x} = -23$- $E_y = -\frac{\partial V}{\partial y} = 27 - 22y = 27 - 22(2) = 27 - 44 = -17$- $E_z = -\frac{\partial V}{\partial z} = 0$ (since $V$ does not depend on $z$)Thus, the electric field $\vec{E} = (-23, -17, 0)$ V/m. The magnitude of $\vec{E}$ is given by $|\vec{E}| = \sqrt{(-23)^2 + (-17)^2 + 0^2} = \sqrt{529 + 289} = \sqrt{818}$, which is approximately 29 V/m.

The Electric Potential at a Point Is Space Is Given