Electric potential at any point is $V = - 5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is
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(d) ${E_x} = - \frac{{dV}}{{dx}} = - ( - 5) = 5;$${E_y} = - \frac{{dV}}{{dy}} = - 3$
and ${E_z} = - \frac{{dV}}{{dz}} = - \sqrt {15} $
${E_{net}} = \sqrt {E_x^2 + E_y^2 + E_z^2} = \sqrt {{{(5)}^2} + {{( - 3)}^2} + {{( - \sqrt {15} )}^2}} = 7$
and ${E_z} = - \frac{{dV}}{{dz}} = - \sqrt {15} $
${E_{net}} = \sqrt {E_x^2 + E_y^2 + E_z^2} = \sqrt {{{(5)}^2} + {{( - 3)}^2} + {{( - \sqrt {15} )}^2}} = 7$
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