Question

A proton, an electron and an \(\alpha\)-particle placed in a uniform electric field experience forces \(F_1\), \(F_2\) and \(F_3\) respectively. Then:

• A. \(F_1 = F_2 = F_3\)
• B. \(F_1 = F_2 \neq F_3\)
• C. \(F_1 > F_2 > F_3\)
• D. \(F_1 < F_2 < F_3\)

Hint:

Force in a uniform field is \(|q|E\); it depends only on charge magnitude. Compare the charges of proton, electron and \(\alpha\)-particle.

Answer 1

The Correct Option is B

Step 1: Concept and formula. In a uniform electric field \(E\), the electric force on a charge \(q\) is \(F = qE\), and its magnitude is \(|q|E\). The force depends only on the magnitude of the charge, not on the mass of the particle.
Step 2: Write the charge of each particle. Proton has charge \(+e\), electron has charge \(-e\), and an \(\alpha\)-particle (helium nucleus) has charge \(+2e\).
Step 3: Substitute to get force magnitudes. \(F_1 = eE\) (proton), \(F_2 = eE\) (electron), \(F_3 = 2eE\) (\(\alpha\)-particle).
Step 4: Compare. Since \(F_1 = F_2 = eE\) and \(F_3 = 2eE\), we get \(F_1 = F_2 \neq F_3\). This is option (ii).
Why other options are wrong: The field is uniform, so mass plays no role, ruling out any strict inequality ordering (options iii and iv). Option (i) is wrong because the \(\alpha\)-particle carries double the charge, so its force is not equal to the others.
\[\boxed{F_1 = F_2 \neq F_3}\]