Question 930: Electrostats & Capacitance

Question

In a region, the potential is represented by V(x, y, z) = 6x $$-$$ 8xy $$-$$ 8y + 6yz,   where $$V$$ is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

Accepted Answer

$$\overrightarrow E  =  - {{\partial V} \over {\partial x}}\widehat i - {{\partial V} \over {\partial y}}\widehat j - {{\partial V} \over {\partial z}}\widehat k$$
$$ =  - \left[ {\left( {6 - 8y} ight)\widehat i + \left( { - 8x - 8 + 6z} ight)\widehat j + \left( {6y} ight)\widehat k} ight]$$
At (1, 1, 1),  $$\overrightarrow E  = 2\widehat i + 10\widehat j - 6\widehat k$$
$$ \Rightarrow \left( {\overrightarrow E } ight) = \sqrt {{2^2} + {{10}^2} + {6^2}}  = \sqrt {140}  = 2\sqrt {35} $$
$$ 	herefore F = q\overrightarrow E  = 2 	imes 2\sqrt {35}  = 4\sqrt {35} $$

Answer

$$6\sqrt 5 $$ N

Answer

30 N

Answer

24 N

Answer

$$4\sqrt {35} $$ N

Electrostats & Capacitance

In a region, the potential is represented by V(x, y, z) = 6x $- 8xy - 8y + 6yz, where V$ is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

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