A Particle of electric charge e and mass m moving under the influence of a constant horizontal electric field E and constant vertical gravitational field described by acceleration due to gravity g. If the particle starts from rest. What will be the trajectory a. parabola b. elliptical c. st line d. circle ?

Question

Answer

Introduction:
In this scenario, a particle of electric charge e and mass m is subjected to a constant horizontal electric field E and a constant vertical gravitational field described by acceleration due to gravity g. The particle starts from rest, and we are required to determine the trajectory of the particle.

Analysis:
To analyze the motion of the particle, we need to consider the forces acting on it. The electric field exerts a force on the particle given by F_electric = eE, where e is the charge and E is the electric field. The gravitational field exerts a force on the particle given by F_gravity = mg, where m is the mass and g is the acceleration due to gravity.

Forces acting on the particle:
- Electric force (F_electric) in the horizontal direction.
- Gravitational force (F_gravity) in the vertical direction.

Motion in the horizontal direction:
The electric force is the only force acting in the horizontal direction, since the particle starts from rest. Therefore, the particle will undergo a constant acceleration in the horizontal direction, given by a_horizontal = F_electric/m = (eE)/m.

Motion in the vertical direction:
The gravitational force is the only force acting in the vertical direction. Since the particle starts from rest, the initial velocity in the vertical direction is zero. Therefore, the particle will undergo free fall motion in the vertical direction, with constant acceleration equal to the acceleration due to gravity, g.

Combined motion:
The motion of the particle can be analyzed by considering the horizontal and vertical motions separately. Since the horizontal and vertical motions are independent of each other, the trajectory of the particle will be a combination of the two motions.

Conclusion:
The trajectory of the particle will be a parabolic path. This can be explained by considering that the horizontal motion is uniformly accelerated motion, while the vertical motion is free fall motion. The combination of these motions results in a parabolic trajectory.

Answer

Parabola

Answer

Parabolic path. The charge moves in resolution of 2 directions one in vertical and because of acceleration of gravity the motion in not uniform in vertical direction. The other it moves in horizontal direction and because of the electric field in horizontal direction the motion is uniform or same throughout the path which charge has travelled

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