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

Question

In a region, the potential is represented by V ( x , y , z ) = 6 x − 8 xy − 8 y + 6 yz , 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 :

TestHub · Accepted Answer

E = − ∂ x ∂ V ​ i ^ − ∂ y ∂ V ​ j ^ ​ − ∂ z ∂ V ​ k ^ = − [( 6 − 8 y ) i ^ + ( − 8 x − 8 + 6 z ) j ^ ​ + ( 6 y ) k ^ ] At ( 1 , 1 , 1 ) , E = 2 i ^ + 10 j ^ ​ − 6 k ^ ⇒ ( E ) = 2 2 + 1 0 2 + 6 2 ​ = 140 ​ = 2 35 ​ ∴ F = q E = 2 × 2 35 ​ = 4 35 ​

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JEE Main 2027 (Class 12)