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A particle of mass m and charge q is thr...

A particle of mass m and charge q is thrown in a region where uniform gravitational field and electric field are present. The path of particle:

A

straight line

B

ellipse

C

parabola

D

circle

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The correct Answer is:
To determine the path of a particle of mass \( m \) and charge \( q \) thrown in a region where a uniform gravitational field and an electric field are present, we can analyze the forces acting on the particle. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Particle**: - The particle experiences two forces: - The gravitational force \( F_g = mg \) acting downwards (where \( g \) is the acceleration due to gravity). - The electric force \( F_e = qE \) acting in the direction of the electric field \( E \) (where \( E \) is the magnitude of the electric field). 2. **Determine the Net Force**: - The net force \( F_{net} \) acting on the particle can be expressed as the vector sum of the gravitational force and the electric force: \[ F_{net} = F_e + F_g \] - Depending on the orientation of the electric field with respect to the gravitational field, the net force will have a specific direction. 3. **Analyze the Direction of the Forces**: - If the electric field is directed upwards and the gravitational field is directed downwards, the net force will be the difference between the two forces: \[ F_{net} = qE - mg \] - If \( qE > mg \), the particle will accelerate upwards; if \( qE < mg \), the particle will accelerate downwards. 4. **Determine the Path of the Particle**: - Since the net force is constant (both \( mg \) and \( qE \) are constants), the particle will experience constant acceleration. - According to Newton's first law, if a particle is subjected to a constant net force, it will move in a straight line. 5. **Conclusion**: - Regardless of the configuration of the electric and gravitational fields, the particle will follow a straight-line trajectory due to the constant net force acting on it. ### Final Answer: The path of the particle will be a straight line.

To determine the path of a particle of mass \( m \) and charge \( q \) thrown in a region where a uniform gravitational field and an electric field are present, we can analyze the forces acting on the particle. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Particle**: - The particle experiences two forces: - The gravitational force \( F_g = mg \) acting downwards (where \( g \) is the acceleration due to gravity). - The electric force \( F_e = qE \) acting in the direction of the electric field \( E \) (where \( E \) is the magnitude of the electric field). ...
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