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A negatively charged particle, initially at rest, is released in a region where a uniform gravitational field and a uniform electric field both act (the two fields are not parallel). Which of the following best describes the shape of the particle's subsequent path?
- A straight line
- A parabola
- A circle
- An ellipse
Correct answer: A straight line
Solution
Each field exerts a force that is constant in both magnitude and direction: gravity gives m*g downward, and the electric field gives a constant q*E force (opposite to E because the charge is negative). Their vector sum is therefore a single constant net force pointing in a fixed direction. A body released from rest experiences acceleration only along this fixed net-force direction, so it speeds up along one straight line. A curved path (parabola, circle, ellipse) would require either an initial velocity transverse to the force or a force that changes direction, neither of which is present here.
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