First slide

Electrostatic potential

Question

Electric potential is given by $V = 6 x - 8 {xy}^{2} - 8 y + 6 yz - 4 z^{2}$ Then electric force acting on 2C point charge placed on origin will be

Moderate

A

2 N
B

6 N
C

8 N
D

20 N

Solution

$E_{x} = - \frac{dV}{dx} = - (6 - 8 y^{2}), E_{y} = - \frac{dV}{dy} = - (- 16 xy - 8 + 6 z) E_{z} = - \frac{dV}{dz} = - (6 y - 8 z) At origin, x = y = z = 0 so, E_{x} = - 6, E_{y} = 8 and E_{z} = 0 \Rightarrow E = \sqrt{E_{x}^{2} + E_{y}^{2}} = 10 N / C Hence, force F = QE = 2 \times 10 = 20 N$

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