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: Key idea. Force in a uniform field is \(F=|q|E\). For a fixed field, force scales directly with charge magnitude, so we only need the ratio of charges.
Step 2: List charge magnitudes as multiples of the elementary charge \(e\). Proton \(=1e\), electron \(=1e\), alpha particle \(=2e\).
Step 3: Form the ratio of forces. \(F_1 : F_2 : F_3 = 1e : 1e : 2e = 1 : 1 : 2\).
Step 4: Read the ratio. The first two forces are equal to each other, while the third is twice as large, so \(F_1 = F_2\) but \(F_3\) is different. Hence \(F_1 = F_2 \neq F_3\), matching option (ii).
\[\boxed{F_1 : F_2 : F_3 = 1 : 1 : 2}\]