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[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.
mv2R=qvBmv2R=qvB
On simplifying the terms, we have:
∴qBm=vR=ω
Step 3: Finding the dimensional formula of angular frequency;