A2 Daily A Level Physics question
In a vacuum tube, a narrow electron beam enters a region of uniform magnetic field at right angles to the field lines and follows a circular path with radius r and period T at constant speed. The magnetic field strength is then increased by 25% while the beam speed is kept the same. Which statement about the new radius r' and period T' is correct?
Answer
The correct answer is A.
Correct: A — r' = 0.80 r and T' = 0.80 T. With speed fixed, a stronger field provides more sideways force so the path tightens (r ∝ 1/B) and T = 2πr/v scales with r, giving both r and T multiplied by 1/1.25 = 0.80. A matches r ∝ 1/B and T ∝ r at fixed speed. B treats a 25% increase in B as a 25% decrease in r and T, instead of the correct inverse factor 1/1.25. C wrongly keeps T unchanged even though T = 2πr/v decreases with r when v is fixed. D wrongly keeps r unchanged; increasing B increases curvature so r must decrease, not stay the same.