Question

A proton and alpha particle enter same magnetic field with same KE at 30° angle. Ratio of pitches is:

• A. 2:1
• B. 1:1
• C. 1:2
• D. 8:1

Hint:

Pitch depends on $\frac{m}{q}$ ratio in magnetic field.

Answer 1

The Correct Option is B

Step 1: Pitch of helical path: \[ P = v_{\parallel} \times T \]
Step 2: Time period: \[ T = \frac{2\pi m}{qB} \]
Step 3: Same KE ⇒ same speed v, same angle ⇒ same $v_{\parallel}$ ratio cancels.
Step 4: Ratio: \[ \frac{P_p}{P_\alpha} = \frac{m_p/q_p}{m_\alpha/q_\alpha} \]
Step 5: \[ m_p = m,\ q_p = e;\quad m_\alpha = 4m,\ q_\alpha = 2e \]
Step 6: \[ \frac{P_p}{P_\alpha} = \frac{m/e}{4m/2e} = 1 \]