Question:

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its:

Updated On: Aug 1, 2022
  • speed
  • mass
  • charge
  • magnetic induction
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The Correct Option is A

Solution and Explanation

In a circular motion in a uniform magnetic field, the necessary centripetal force to the charged particle is provided by the magnetic force, i.e., $ \frac{m{{v}^{2}}}{r}=qvB $ $ r=\frac{mv}{qB} $ Thus, the time period T is $ T=\frac{2\pi r}{v} $ $ =\frac{2\pi m}{qB} $ So, Tis independent of its speed.
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Concepts Used:

Magnetic Field

The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.

A magnetic field can be presented in two ways.

  • Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
  • Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.

Properties of Magnetic Field Lines

  • Magnetic field lines never cross each other
  • The density of the field lines indicates the strength of the field
  • Magnetic field lines always make closed-loops
  • Magnetic field lines always emerge or start from the north pole and terminate at the south pole.