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The electric potential at a point (x, y,...

The electric potential at a point (x, y, z) is given by `V = -x^(2)y - xz^(3) +4`. Find the intensity of electric field `vec(E )` at that point.

Text Solution

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`E_(x) = -(dV)/(dx) = 2xy + z^(3), E_(y) = -(dV)/(dy) = x^(2)`
`E_(z) = -(dV)/(dz) = 3xz^(2)`
`:. Vec(E ) = E_(x) hat(i) + E_(y)hat(j)+E_(z)hat(k) = (2xy + z^(3))hat(i) + x^(2)hat(j) + 3xz^(2)hat(k)`.
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