Which of the following particles will experience the maximum magnetic force (magnitude) when projected with the same velocity perpendicular to the magnetic field?
- Electron
- Proton
- He+
- Li++
The Correct Option is D
Approach Solution - 1
The magnetic force on a charged particle is given by:
F = qvB sinθ
Where θ = 90° for perpendicular projection ⇒ sinθ = 1
Thus, the force depends on the charge q when v and B are constant.
Comparing the charges:
| Particle | Charge (q) |
|---|---|
| Electron | -e |
| Proton | +e |
| He+ | +e |
| Li++ | +2e |
Since Li++ has the highest charge magnitude (2e), it will experience the maximum force.
The particle that will experience maximum magnetic force is Li++.
Correct option: (4) Li++
Approach Solution -2
The magnetic force on a charged particle moving in a magnetic field is given by the Lorentz force law:
\(F=qvBsinθ\)
where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.
Since all particles are moving perpendicular to the magnetic field, sinθ=1, so the force is directly proportional to the charge of the particle.
Electron: charge = −e; Proton: charge = +e; He+ (Helium ion): charge = +e (since it’s lost one electron); Li++ (Lithium ion): charge = +2e (since it has lost two electrons).
The particle with the largest charge will experience the greatest force. Since Li++ has a charge of +2e, it will experience the maximum force.
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