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5. The electric potential V in a region of space is given by V(x, y, z) = A(x² - 3y² + z²), where
A is a constant. a) Derive an expression for the electric field E at any point in this region. b)
The work done by the field when a 1.50µC test charge moves from the point (x, y, z) = (0, 0,
0.250m) to the origin is measured to be 6.00 x10-5J. Determine A. c) Determine the electric
field at the point (0, 0, 0.250m).

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