Mathematical routines (MR)
Proton deflected between charged parallel plates
- Unit 10
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.
The question
Two horizontal, parallel conducting plates, each a square 5.0 cm on a side, are 2.0 cm apart. The top plate is connected to the positive terminal of a 150 V battery and the bottom plate to the negative terminal. A proton enters the space between the plates midway between them, moving horizontally at 5.0 × 10⁵ m/s, parallel to the plates, and travels the full 5.0 cm length of the plates without hitting either one. Ignore gravitational forces and edge effects. Use proton mass 1.67 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C and ε₀ = 8.85 × 10⁻¹² C²/(N·m²).
Suggested time: 22 minutes
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Part (a)
2 pointsDescribe the electric field between the plates, the force diagram for the proton while it is between the plates, and the shape of the proton's path.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
3 pointsDerive an expression for the vertical distance y the proton is deflected by the time it reaches the end of the plates, in terms of the proton's charge q and mass m, the potential difference ΔV, the plate separation d, the plate length ℓ, and the initial speed .
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
2 pointsCalculate (i) the vertical deflection of the proton at the end of the plates and (ii) the increase in the proton's kinetic energy while it is between the plates.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
2 pointsAn alpha particle (charge +2e, mass about 4 times the proton's mass) enters the plates in the same way, at the same speed. Is its vertical deflection at the end of the plates greater than, less than, or equal to the proton's? Justify your claim using your expression from part (b).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
1 pointCalculate the magnitude of the charge on each plate.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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