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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.
- 2i
- -2i
- i + j
- -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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