In a region the potential is represented by V x , y , z = 6 x - 8 x y - 8 y + 6 y z , where V is in volts and x , y , z , are in meters. The electric force experienced by a charge of 2 coulombs situat

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In a region the potential is represented by V x , y , z = 6 x - 8 x y - 8 y + 6 y z , where V is in volts and x , y , z , are in meters. The electric force experienced by a charge of 2 coulombs situated at point 1 , 1 , 1 is:NEET 2014

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Potential in the space varies as V x , y , z = 6 x - 8 x y - 8 y + 6 y z . Electric field is given by, E x = - ∂ V ∂ x = - 6 + 8 y E y = - ∂ V ∂ y = 8 x + 8 - 6 z E z = - ∂ V ∂ z = - 6 y E → = - 6 + 8 y i ^ + 8 x + 8 - 6 z j ^ - 6 y k ^ Putting the value of the position we get, E → 1 , 1 , 1 = 2 i ^ + 10 j ^ - 6 k ^ Magnitude is given by, E → = 2 35 N C - 1 Force on the charge is given by, F = q E = 2 × 2 35 = 4 35 N

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