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Starting from a point and moving in a direction that makes an angle theta with the +x-axis, the potential gradient is found to be dV/dr = 2 cos(theta). Determine the magnitude and direction of the electric field at that point.

1. 2i
2. -2i
3. i + j
4. -i + j

Correct answer: -2i

Solution

The directional derivative varying as 2 cos(theta) means the gradient vector has magnitude 2 directed along +x (so its projection onto a direction at angle theta is 2 cos theta). The electric field is the negative gradient, giving E = -2 i.

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