A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass?
(Curves are drawn schematically and are not to scale).

Solution

Physics sir · 4 steps

It starts from rest under a constant net force, so it moves in a straight line along that force.

1. Two constant forces. The electric force qE acts along +x and gravity mg acts along +y (downward in the figure). Both are constant, so each direction has a constant acceleration: aₓ = qE/m and a_y = g.
2. Released from rest. The mass is released, so its initial velocity is zero in both directions. Starting from rest, x = 1/2aₓ t² and y = 1/2g t².

   y/x = (1/2g t²)/(1/2qE/m t²) = mg/qE = constant

3. Shape of the path. Since t² cancels, y = (mg/qE)x. That is the equation of a straight line through the starting point, along the direction of the net force.
4. So. The trajectory is a straight line through the origin, which is option (a).

The idea to keep. A curved path needs a starting velocity that is not along the force. If a body starts from rest under a constant net force, it moves in a straight line along that force.

Answer from the NTA final answer key. Solution by PrepWiser.