If potential at a point P ( 1.1,1) is given by the relation $V p = x^{2} + y^{2} + 2_{z}$ ,then calculate the electric field at P.

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Solution

Potential is given by:

$V_{P} = x^{2} + y^{2} + 2 z$

$∵ \to E = - (\frac{\partial V}{\partial x}^i + \frac{\partial V}{\partial y}^j + \frac{\partial V}{\partial z}^k)$

$\frac{\partial V}{\partial x} = 2 x$

$\frac{\partial V}{\partial y} = 2 y$

$\frac{\partial V}{\partial z} = 2$

$s o,$

$E_{(1, 1, 1)} = - (2 x + 2 y + 2)$

$E_{(1, 1, 1)} = - 6 N / C$
Electric field at point P is 6 N/C.

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