Magnetic Force on a Moving Charge Lorentz Force - UNSOLVED PRACTICE SET

Q7. State the expression for the Lorentz force on a charged particle. Explain the significance of the cross product in the magnetic force term.

Q8. A charge q = +2 μC moves with velocity v = (3î + 4ĵ) m/s in a magnetic field B = 2k̂ T. Calculate the magnetic force on the charge.

Q9. Why does a magnetic field change the direction of a moving charged particle but not its speed? Explain using the concept of work done.

Q10. An electron enters a uniform magnetic field perpendicular to its velocity. Describe the path it follows. What provides the centripetal force?

Q11. A charged particle moves with velocity v at angle θ to a uniform magnetic field B. Write the expression for the magnetic force and identify the components of velocity that contribute to it.

Q12. In a cathode ray tube (like old TV screens), how does a magnetic field deflect the electron beam? Explain the direction of deflection.

Q13. Derive the expression for the magnetic force on a moving charge. Explain why the force is perpendicular to both velocity and magnetic field. Use Fleming's left-hand rule to determine the direction of the force.

Q14. Explain the Lorentz force when a charged particle moves in the presence of both electric and magnetic fields. How can these fields be arranged so that the net force on the particle is zero? What is this condition called and where is it used?

Q15. An alpha particle (charge +2e, mass 6.64 × 10⁻²⁷ kg) enters a uniform magnetic field B = 0.5 T with velocity v = 2 × 10⁶ m/s perpendicular to the field.

(a) Calculate the magnetic force on the alpha particle.  

(b) Calculate the radius of the circular path it follows.  

(c) Calculate the time period of revolution.  

(d) If the velocity is doubled, how do the force, radius, and time period change?

[Given: e = 1.6 × 10⁻¹⁹ C]

Q16. In a school physics lab, a student uses a velocity selector to study charged particles. The velocity selector has uniform electric field E = 2 × 10⁴ N/C (downward) and uniform magnetic field B = 0.5 T (into the page).

(a) Draw the free body diagram for a positive charge moving through the velocity selector.  

(b) Calculate the velocity of particles that pass through undeflected.  

(c) If protons enter with this velocity, calculate the magnetic force and electric force on them. Show that they are equal and opposite.  

(d) If electrons enter with twice this velocity, which force dominates? Describe their trajectory.  

(e) Explain why a velocity selector is essential in mass spectrometers.

[Given: e = 1.6 × 10⁻¹⁹ C]

Q17. A particle of mass m = 1.67 × 10⁻²⁷ kg and charge q = +1.6 × 10⁻¹⁹ C is accelerated through a potential difference V = 2000 V and then enters a uniform magnetic field B = 0.4 T perpendicular to its velocity.

(a) Calculate the speed of the particle as it enters the magnetic field.  

(b) Calculate the radius of the circular path.  

(c) Calculate the frequency of revolution (cyclotron frequency).  

(d) If the particle were a deuteron (same charge, twice the mass), how would the radius and frequency change?  

(e) A student claims that heavier particles always have larger radii. Is this always true? Explain.

Q18. A beam of particles containing electrons, protons, and alpha particles, all with the same kinetic energy, enters a uniform magnetic field B = 0.3 T perpendicular to the beam.

(a) Calculate the ratio of the radii of their circular paths.  

(b) Calculate the ratio of their time periods.  

(c) If the beam is split into three separate beams after traveling 180°, what is the separation between the electron beam and the proton beam?  

(d) Explain how this principle is used in mass spectrometers to identify isotopes.  

(e) Why can't a uniform magnetic field alone be used to separate particles by mass if they have different charges?

[Given: mₑ = 9.1 × 10⁻³¹ kg, mₚ = 1.67 × 10⁻²⁷ kg, m_α = 6.64 × 10⁻²⁷ kg, e = 1.6 × 10⁻¹⁹ C]