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Sagot :
The electric field at (x,y,z) its equal to the negative of the gradient if the electric potential.
We have
V(x, y, z) = 2x² - 3y² + 5z
so
E(x, y, z) = -grad(V) = -(dV/dx i + dV/dy j + dV/dz k)
where d/d(variable) is meant to be a partial derivative with respect to that variable. The partial derivatives are
dV/dx = 4x
dV/dy = -6y
dV/dz = 5
and so the electric field at any point is
E(x, y, z) = -4x i + 6y j - 5k
and at (3, 4, 5) it is
E(3, 4, 5) = -12i + 24j - 5k
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