Electric potential is given by $V = 6 x - 8 {x y}^{2}$ . Then electric force acting on $2 C$ point charge placed at the origin will be

2 N

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6 N

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8 N

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12 N

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Solution

The correct option is D $12 N$
$V = 6 x - 8 x y^{2}$
$Q = 2 C$
$\begin{matrix} E_{x} = - \frac{d v}{d x} = 6 - 8 x y^{2} = 6 E_{y} = - \frac{d v}{d y} = - 8 \times x \times 2 y = 0 E = \sqrt{{E_{x}}^{2} + {E_{y}}^{2}} = \sqrt{{(6)}^{2} + 0} = 6 F = Q E F = 2 \times 6 = 12 N \end{matrix}$

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Electric potential is given by $V = 6 x - 8 {x y}^{2}$ . Then electric force acting on $2 C$ point charge placed at the origin will be

The correct option is D $12 N$
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$\begin{matrix} E_{x} = - \frac{d v}{d x} = 6 - 8 x y^{2} = 6 E_{y} = - \frac{d v}{d y} = - 8 \times x \times 2 y = 0 E = \sqrt{{E_{x}}^{2} + {E_{y}}^{2}} = \sqrt{{(6)}^{2} + 0} = 6 F = Q E F = 2 \times 6 = 12 N \end{matrix}$