Question

An electron is moving in a circular orbit in a magnetic field of 2 × 10^-4 weber/m². Its time period of revolution is:
1. 1.79 × 10^-7 sec
2. 3.5 × 10-7 sec
3. 7 × 10-7 sec
4. 2.75 × 10-7 sec

Answer 1

Correct Answer - Option 1 : 1.79 × 10^-7 sec

CONCEPT:

Lorentz force:

• It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force on the charged particle is called the Lorentz force and is given by

​⇒ FL = qE + qvBsinθ 

• A charged particle experiences a force when it moves in a magnetic field.
• The magnetic force is given as,

​
⇒ F = qvBsinθ

• When the velocity of a charged particle is perpendicular to a magnetic field, it describes a circle.

Time period:​

• Time is taken by a charged particle to complete one revolution is called the time period.
• The time period is given as,

\(⇒ T=\frac{2\pi m}{qB}\)

Where, F =  force due to magnetic field, m = mass, q = magnitude of charge, v = speed of charge, E = electric field, B = magnetic field and θ = angle between v and B

CALCULATION:

​Given q = 1.6 × 10^-19 C, m = 9.1 × 10-31 kg, and B = 2 × 10-4 weber/m2

• The time period is given as,

\(⇒ T=\frac{2\pi m}{qB}\)

\(⇒ T=\frac{2\pi \times9.1\times10^{-31}}{1.6\times10^{-19}\times2\times10^{-4}}\)

⇒​ T = 1.79 × 10-7 sec

• Hence, option 1 is correct.