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When a charged particle is projected per...

When a charged particle is projected perpendicular to a uniform magnetic field, it describes a circular path in which :

A

its speed remains constant.

B

its velocity remains constant.

C

its momentum remains constant.

D

its kinetic energy increases.

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To solve the question regarding the motion of a charged particle projected perpendicular to a uniform magnetic field, we can break it down into the following steps: ### Step-by-Step Solution: 1. **Understanding the Motion**: When a charged particle (like an electron or proton) is projected into a magnetic field, the force acting on it is due to the magnetic field. This force is known as the Lorentz force. 2. **Direction of the Force**: The Lorentz force acts perpendicular to both the velocity of the charged particle and the direction of the magnetic field. According to the right-hand rule, if you point your thumb in the direction of the velocity (the motion of the particle) and your fingers in the direction of the magnetic field, your palm will face the direction of the force acting on a positive charge. 3. **Circular Motion**: Since the force is always perpendicular to the velocity, it does not do any work on the particle. This means that the speed of the particle remains constant, but its direction changes continuously, causing the particle to move in a circular path. 4. **Kinetic Energy**: Because the work done by the magnetic field is zero (as the force is perpendicular to the displacement), the kinetic energy of the particle remains constant. The formula for kinetic energy is \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the speed of the particle. Since \( v \) remains constant, the kinetic energy does not change. 5. **Conclusion**: Therefore, when a charged particle is projected perpendicular to a uniform magnetic field, it describes a circular path with constant speed and constant kinetic energy. ### Final Answer: The charged particle revolves in a circular path with constant speed and constant kinetic energy. ---
To solve the question regarding the motion of a charged particle projected perpendicular to a uniform magnetic field, we can break it down into the following steps: ### Step-by-Step Solution: 1. **Understanding the Motion**: When a charged particle (like an electron or proton) is projected into a magnetic field, the force acting on it is due to the magnetic field. This force is known as the Lorentz force. 2. **Direction of the Force**: The Lorentz force acts perpendicular to both the velocity of the charged particle and the direction of the magnetic field. According to the right-hand rule, if you point your thumb in the direction of the velocity (the motion of the particle) and your fingers in the direction of the magnetic field, your palm will face the direction of the force acting on a positive charge. ...
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