Question

Following charged particles are projected perpendicular to a uniform magnetic field with same velocity. Which one will experience maximum force?

• A. electron
• B. proton
• C. \(\alpha\) particle
• D. deuteron

Hint:

\(F = qvB\) with same \(v,B\); largest charge wins, and the \(\alpha\) particle carries \(2e\).

Answer 1

The Correct Option is C

Step 1: Write the magnetic force on a moving charge.
\[ F = q v B \sin\theta \]
Here the velocity is perpendicular to \(B\), so \(\theta = 90^\circ\) and \(\sin\theta = 1\):
\[ F = q v B \]
Step 2: Note what is common and what varies.
Speed \(v\) and field \(B\) are the same for all four particles, so the force depends only on the magnitude of charge \(q\).
Step 3: Compare the charges.
Electron: \(|q| = e\); proton: \(q = e\); deuteron: \(q = e\); \(\alpha\) particle: \(q = 2e\).
Step 4: The \(\alpha\) particle carries the largest charge \(2e\), so it experiences the maximum force. Mass is irrelevant to the instantaneous force here.
\[\boxed{\alpha\text{ particle}}\]