1. \(\overrightarrow F=q(\overrightarrow V\times \overrightarrow B)\)
2. Consider a rod of uniform cross section ‘A’ and length ‘ I ’. Let ’n’ be the number of electrons per unit volume (number density). ‘vd ’ be the drift velocity of electrons for steady current ‘I’.
Total number of electrons in the entire volume of rod = nAI
Charge of total electrons = nA I .e ‘e’ is the charge of a single electron.
The Lorentz force on electrons,
\(\overrightarrow F = nAle(\overrightarrow V_d\times \overrightarrow B)\)
\(\overrightarrow F=nAV_de(\overrightarrow l\times \overrightarrow B)\)
\(\overrightarrow F=I(\overrightarrow l\times \overrightarrow B)\) \( (I = neAV_d)\)
3. Yes, When an electron moves in a magnetic field with an angle θ, the electron undergoes for helical motion. The velocity of electron has two components, usinθ and ucosθ.
The component usinθ produces circular motion and ‘ucosθ’ produces translational motion. The combined effect of circular motion and translation motion will be helical motion.