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A uniform electric field of magnitude E lies in the x-y plane, making angle theta with the x-axis (as in the figure). Find the potential difference V(O) - V(A) between the origin O and the point A(d, d, 0).

1. Ed (cos(theta) + sin(theta))
2. -Ed (sin(theta) - cos(theta))
3. sqrt(2) Ed
4. none of these

Correct answer: Ed (cos(theta) + sin(theta))

Solution

For a uniform field, V(O) - V(A) = E. r_(O to A) where r is the vector from O to A. With E = (E cos(theta), E sin(theta), 0) and the vector from O to A = (d, d, 0), the dot product is E*d*cos(theta) + E*d*sin(theta) = Ed(cos(theta) + sin(theta)).

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