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Q.

The electric potential (in volt) in a region is given by V=6x−8xy2−8y+6yz−4x2Then electric force acting on a point charge of 2C placed at the origin will be

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a

2 N

b

6 N

c

8 N

d

20 N

answer is D.

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Detailed Solution

E→=∇→V⇒E→=−i^∂U∂x+j^∂U∂y+k^∂U∂z ∂U∂x=6−8y2−8x∂U∂y=−16xy−8+6z∂U∂z=6yAt(0,0,0)∂U∂x=6,∂U∂y=−8,∂U∂z=0 ⇒|E→|(0,0,0)=−6i^+8j^⇒|E→|=10NC−1⇒|F→|=q|E→|⇒|F→|=20N
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