In a region, the potential is represented by V ( x , y , z ) = 6 x − 8 x y − 8 y + 6 yz , where V is in volts and x , y , z are in meters. The electric force experienced by a charge of 2 coulomb situa

Question

In a region, the potential is represented by V ( x , y , z ) = 6 x − 8 x y − 8 y + 6 yz , where V is in volts and x , y , z are in meters. The electric force experienced by a charge of 2 coulomb situated at the point ( 1 , 1 , 1 ) is N 35 ​ N. What is N ?

TestHub · Accepted Answer

E = − ∇ V = − [( 6 − 8 y ) i ^ + ( − 8 x − 8 + 6 z ) j ^ ​ + ( 6 y ) k ^ ] At ( 1 , 1 , 1 ) : E = − [ − 2 i ^ − 10 j ^ ​ + 6 k ^ ] ∣ F ∣ = q ∣ E ∣ = 2 4 + 100 + 36 ​ = 2 140 ​ = 4 35 ​ N N = 4 Printed key: 4.00.

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