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In a uniform magnetic field, a charged particle moves in a circular path. What i

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Question: In a uniform magnetic field, a charged particle moves in a circular path. What is the relationship between the radius of the path and the speed of the particle? (2022)

Options:

  1. Directly proportional
  2. Inversely proportional
  3. No relation
  4. Quadratic relation

Correct Answer: Directly proportional

Exam Year: 2022

Solution: 

The radius of the circular path is directly proportional to the speed of the charged particle in a uniform magnetic field.

In a uniform magnetic field, a charged particle moves in a circular path. What i

Practice Questions

Q1
In a uniform magnetic field, a charged particle moves in a circular path. What is the relationship between the radius of the path and the speed of the particle? (2022)
  1. Directly proportional
  2. Inversely proportional
  3. No relation
  4. Quadratic relation

Questions & Step-by-Step Solutions

In a uniform magnetic field, a charged particle moves in a circular path. What is the relationship between the radius of the path and the speed of the particle? (2022)
  • Step 1: Understand that a charged particle moving in a magnetic field experiences a force that causes it to move in a circular path.
  • Step 2: Recognize that the speed of the particle affects how far it travels in one complete circle.
  • Step 3: Realize that if the speed of the particle increases, it needs a larger radius to maintain the circular motion without changing the magnetic field strength.
  • Step 4: Conclude that the radius of the circular path increases as the speed of the charged particle increases, meaning they are directly proportional.
  • Magnetic Force and Circular Motion – In a uniform magnetic field, a charged particle experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path. The radius of this path is influenced by the speed of the particle.
  • Lorentz Force – The force acting on a charged particle in a magnetic field is given by the Lorentz force equation, which relates the charge, velocity, and magnetic field strength.
  • Centripetal Acceleration – The relationship between the radius of the circular path, the speed of the particle, and the magnetic field strength can be derived from the centripetal acceleration formula.
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