In a region, the potential is represented by V(x, y,

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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 :

1. 6√5N
2. 30 N
3. 24 N
4. 4√35N

Correct Option: D

^→E = -	∂V	î +	∂V	ĵ +	∂V	̂k
	∂x		∂y		∂z

= - [(6 - 8y)î + (-8X - 8 + 6z)ĵ + (6y)̂k]
At (1,1,1), ^→E(1,1,0) = 2î + 10ĵ - 6̂k
⇒ (^→E) = √2² + 10² + 6² = √140 = 2√35
∴ F = q^→E = 2 × 2√35 = 4√35