A2 Daily A Level Physics question
In a lab mass filter, a narrow beam of K+ ions (charge +e) enters a region of uniform magnetic field B at right angles with speed v and follows a circular arc to a screen. The setup is then changed to a beam of Rb+ ions that have twice the mass; at the same time the magnetic field is halved and the ion speed is doubled. The beams are always perpendicular to the field. Compared with the original K+ path, which statement about the Rb+ path must be true (side of bending and radius)?
Answer
The correct answer is A.
Correct: A — The Rb+ path bends to the same side as the K+ path and has a radius eight times larger. A is correct because both ions are positively charged so the deflection side is the same; using proportional reasoning for circular motion in a magnetic field, radius ∝ (m v)/(q B), so changing to 2m, 2v, and B/2 multiplies the radius by (2×2)/(1/2) = 8; as a limiting check, reducing B makes paths less curved (larger radius), consistent with this result. B is wrong because the side only flips for opposite charge (not the case here), and the radius does not stay the same when m, v, and B all change. C is wrong because increasing m and v and reducing B all act to increase, not decrease, the radius; four times smaller is the opposite trend. D is wrong because the side would not reverse for a positive ion, and halving B increases, not halves, the radius (it contributes a factor of 2 increase).