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The electric potential in a region is V = 343/r, where r is the distance from the origin. Find the electric field at the point r-vector = 3i + 2j + 6k.

1. 21i + 14j + 42k
2. 3i + 2j + 6k
3. (1/7)(3i + 2j + 6k)
4. -(3i + 2j + 6k)

Correct answer: 3i + 2j + 6k

Solution

V = 343/r gives radial field magnitude E = -dV/dr = 343/r² directed along r-hat. Here |r| = sqrt(9+4+36) = 7, so E_mag = 343/49 = 7. The unit vector is (3i+2j+6k)/7, so E = 7 * (3i+2j+6k)/7 = 3i + 2j + 6k.

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