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The electric potential in the space at any point is given by V(x,y,z) = (2xy + y2z + x2yz) volt, where x, y and z are in metre. Then y component of electric field at the point (2, 3, 1) will be

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\(V = (2xy + y^2z + x^2yz)\)

\(E = -\triangledown V\)

\(= -\left(\frac\partial{\partial x} + \frac\partial {\partial y } + \frac\partial {\partial z}\right)V\)

\(= -\left(\frac{\partial V}{\partial x} + \frac{\partial V} {\partial y } + \frac{\partial V} {\partial z}\right)\)

\(= - [(2y + 2xyz) + (2x + 2yz + x^2y) + (y^2 + x^2y)]\)

\(= - [(6 + 12)+ (4 + 2 \times 3 \times 1 + 4 \times 3)+ ( 9 + 4 \times 3)]\)

\(= -[18+22+21]\)

\(= -[18+ 43]\)

\(= -[61]\,N/C\)

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