The electric potential (in volt) a region given by
$V = 6 x - 8 x y^{2} - 8 y + 6 y z - 4 x^{2}$ Then electric force acting on a point charge of 2c placed at the origin will be

2 N

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6 N

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8 N

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20 N

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Solution

The correct option is D 20 N
$\begin{matrix} g i v e n, V = 6 x - 8 x y^{2} - 8 y + 6 y z - 4 x^{2} A l o n g x - a x i s = \frac{d v}{d x} = 6 - 8 y^{2} - 8 x A l o n g Y - a x i s = \frac{d v}{d x} = 16 x y - 8 + 6 z A l o m g z - a x i s = \frac{d v}{d x} = 6 y A t o r i g i o n, (\frac{d v}{d x}, \frac{d v}{d y}, \frac{d v}{d z}) = (6, - 8, 0) N e t E l e c t r i c f i e l d = \sqrt{6^{2} + {(- 8)}^{2}} = 10 F o r c e a c t i n g = q E = 2 \times 10 = 20 N \end{matrix}$

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The electric potential (in volt) a region given byV=6x−8xy2−8y+6yz−4x2 Then electric force acting on a point charge of 2c placed at the origin will be

The correct option is D 20 Ngiven,V=6x−8xy2−8y+6yz−4x2Alongx−axis=dvdx=6−8y2−8xAlongY−axis=dvdx=16xy−8+6zAlomgz−axis=dvdx=6yAtorigion,(dvdx,dvdy,dvdz)=(6,−8,0)NetElectricfield=√62+(−8)2=10Forceacting=qE=2×10=20N

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$V = 6 x - 8 x y^{2} - 8 y + 6 y z - 4 x^{2}$ Then electric force acting on a point charge of 2c placed at the origin will be