1. Tardigrade
  2. Question
  3. Physics
  4. Electric potential is given by V=6x- 8xy2 - 8y + 6yz - 4Z2 Then electric force (in N) acting on 2C point charge placed on origin will be .

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Q. Electric potential is given by $V=6x- 8xy^2 - 8y + 6yz - 4Z^2$ Then electric force (in $N$) acting on $2C$ point charge placed on origin will be _________ .

Electrostatic Potential and Capacitance

Solution:

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