A2 Daily A Level Physics question
A proton moves at a constant velocity `v` through a region of space. The region contains a uniform electric field of strength `E` and a uniform magnetic field of strength `B`. The fields and the proton's velocity are all mutually perpendicular. The magnetic field strength is then suddenly halved, while the electric field strength remains constant. Which statement best describes the initial net force on the proton immediately after this change?
Answer
The correct answer is A.
Correct: A — The net force acts in the direction of the electric force and has a magnitude equal to the new magnetic force. For the initial constant velocity, the electric force (F_E) and magnetic force (F_B) must be equal and opposite. When the magnetic field strength is halved, the new magnetic force is F_B' = F_B / 2. The net force is the vector sum F_E + F_B', which has a magnitude of F_E - F_B' = F_B - F_B/2 = F_B/2. This net force is in the direction of the larger force (F_E) and, by a subtle coincidence of the maths, has a magnitude exactly equal to the new magnetic force (F_B/2). B is incorrect because it ignores the presence of the remaining magnetic force; the net force is the difference between the two forces, not the full electric force. C is incorrect because halving one of the field strengths explicitly breaks the force balance; velocity cannot change instantaneously to compensate for the change in force. D is incorrect because it identifies the wrong direction for the net force; since the electric force is now greater than the magnetic force, the net force must be in the direction of the electric force.