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The electric potential at any point in space is V = -5x + 3y + sqrt(15) z. Find the magnitude of the electric field.

1. 3*sqrt(2)
2. 4*sqrt(2)
3. 5*sqrt(2)
4. 7

Correct answer: 7

Solution

From V = -5x + 3y + sqrt(15) z: Ex = -dV/dx = 5, Ey = -dV/dy = -3, Ez = -dV/dz = -sqrt(15). Magnitude = sqrt(5² + 3² + 15) = sqrt(25 + 9 + 15) = sqrt(49) = 7.

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