Ncert Exercises & Solutions

A charged particle of charge e and mass m is moving in an electric field E and magnetic field B. Construct dimensionless quantities and quantities of dimension ${[T]}^{- 1}$ .

Hint: The particle may do a helical motion.

Step 1: No dimensionless quantity can be constructed using given quantities.
Step 2: For a charged particle moving perpendicular to the magnetic field, the magnetic Lorentz forces provide necessary centripetal force for revolution.

\frac{{mv}^{2}}{R} = qvB

On simplifying the terms, we have:

∴ \frac{qB}{m} = \frac{v}{R} = ω

Step 3: Finding the dimensional formula of angular frequency;

∴ [ω] = [\frac{qB}{m}] = [\frac{v}{R}] = [T]^{- 1}

This is the required expression.

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions