INPhO 2026, Теория — Задача 1. Find the flaw

Indian National Physics Olympiad (INPhO)-2026 · Question Paper · 1 февруари 2026 г. · 12 т.

Внимание: Бележка към темата

Matching original question and official key booklets are retained in full. The separate blank Answer Booklet, Summary Answersheet copies and blank graph paper referred to in the questions are absent from the archive; the supplied completed Kepler/glass answer-sheet illustrations remain in the key. Native question pages7 and9 are blank. Question6 says photographs on the next page although its photos occur on native p10 after blank p9. Printed source errors/conventions are preserved and attributed locally: P2 negative dM followed by positive boxed dUm and changing absolute-work notation; P3 Qa=-W followed by positive released heat, dropped-mass wording and P0/V0 notation; P4 derivative/height signs, c/cs and time-delay description; P5 intermediate phiP versus final phiC, log log and r/logarithm numerical scales. The graph/grid pixels and printed fitted results are source data, not newly calculated measurements.

Question booklet · Instructions and Table of Constants

Indian National Physics Olympiad (INPhO)-2026

HOMI BHABHA CENTRE FOR SCIENCE EDUCATION · Tata Institute of Fundamental Research · V. N. Purav Marg, Mankhurd, Mumbai, 400 088

Question Paper

Date: 01 February 2026 · Time: 09:00–12:00 (3 hours) · Maximum Marks: 75

Roll Number: □□□□ – □□□□ – □□□□

Instructions

  1. This booklet consists of 10 pages and total of 6 questions. Write roll number at the top wherever asked.
  2. Booklet to write the answers is provided separately. Instructions to write the answers are on the Answer Booklet.
  3. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.
  4. Take as many data points as possible for the analysis.
  5. Please submit the Answer Sheet at the end of the examination. You may retain the Question Paper.
  6. Except for writing your roll number, no rough work or scribbling is allowed on the question paper.

Table of Constants

QuantitySymbolValue
Speed of light in vacuumcc3.00×108 m⋅s−13.00\times10^8\ \mathrm{m\cdot s^{-1}}
Magnitude of electron chargeee1.60×10−19 C1.60\times10^{-19}\ \mathrm C
Avogadro’s numberNAN_A6.022×1023 mol−16.022\times10^{23}\ \mathrm{mol^{-1}}
Acceleration due to gravitygg9.81 m⋅s−29.81\ \mathrm{m\cdot s^{-2}}
Universal Gas ConstantRR8.31 J⋅K−1⋅mol−18.31\ \mathrm{J\cdot K^{-1}\cdot mol^{-1}}
RR0.0821 l⋅atm⋅mol−1⋅K−10.0821\ \mathrm{l\cdot atm\cdot mol^{-1}\cdot K^{-1}}
Boltzmann constantkBk_B1.3806×10−23 J⋅K−11.3806\times10^{-23}\ \mathrm{J\cdot K^{-1}}
Permeability constantμ0\mu_04π×10−7 H⋅m−14\pi\times10^{-7}\ \mathrm{H\cdot m^{-1}}
One Atmospheric pressureatm1.013×105 Pa1.013\times10^5\ \mathrm{Pa}
Question Number123456Total
Maximum Marks12121110181275
Solution booklet · Instructions, constants and alternate-method note

Indian National Physics Olympiad (INPhO)-2026

HOMI BHABHA CENTRE FOR SCIENCE EDUCATION · Tata Institute of Fundamental Research · V. N. Purav Marg, Mankhurd, Mumbai, 400 088

Question Paper

Date: 01 February 2026 · Time: 09:00–12:00 (3 hours) · Maximum Marks: 75

Roll Number: □□□□ – □□□□ – □□□□

Instructions

  1. This booklet consists of 21 pages and total of 6 questions. Write roll number at the top wherever asked.
  2. Booklet to write the answers is provided separately. Instructions to write the answers are on the Answer Booklet.
  3. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.
  4. Take as many data points as possible for the analysis.
  5. Please submit the Answer Sheet at the end of the examination. You may retain the Question Paper.
  6. Except for writing your roll number, no rough work or scribbling is allowed on the question paper.

Table of Constants

QuantitySymbolValue
Speed of light in vacuumcc3.00×108 m⋅s−13.00\times10^8\ \mathrm{m\cdot s^{-1}}
Magnitude of electron chargeee1.60×10−19 C1.60\times10^{-19}\ \mathrm C
Avogadro’s numberNAN_A6.022×1023 mol−16.022\times10^{23}\ \mathrm{mol^{-1}}
Acceleration due to gravitygg9.81 m⋅s−29.81\ \mathrm{m\cdot s^{-2}}
Universal Gas ConstantRR8.31 J⋅K−1⋅mol−18.31\ \mathrm{J\cdot K^{-1}\cdot mol^{-1}}
RR0.0821 l⋅atm⋅mol−1⋅K−10.0821\ \mathrm{l\cdot atm\cdot mol^{-1}\cdot K^{-1}}
Boltzmann constantkBk_B1.3806×10−23 J⋅K−11.3806\times10^{-23}\ \mathrm{J\cdot K^{-1}}
Permeability constantμ0\mu_04π×10−7 H⋅m−14\pi\times10^{-7}\ \mathrm{H\cdot m^{-1}}
One Atmospheric pressureatm1.013×105 Pa1.013\times10^5\ \mathrm{Pa}
Question Number123456Total
Maximum Marks12121110181275

Please note that alternate/equivalent methods and different ways of expressing final solutions may exist. A correct method will be suitably awarded.

Условие

Consider a non-conducting, charged, thin cubical shell with a uniform surface charge density. Consider the plane ABCD, which vertically and symmetrically divides the cubical shell (see figure).

Native cubical shell and symmetry plane ABCD with complete x,y,z axes and all corner labels.

Six students independently solved for the electric field on the plane ABCD and presented six different answers, shown below in Figs. (a) to (f), each approximately depicting the electric field lines in the ABCD plane (the field line arrows are not shown). Consider each of the six answers, and for each, give

  • at least one reason (based on a physics argument), explaining why it is incorrect

OR

  • at least two reasons why it could be correct.

Note that you are not required to obtain the correct depiction of the electric field or to provide a detailed derivation in this question.

In none of the figures, adjacent field lines touch or intersect each other, although they may appear to do so in Fig. (c) and Fig. (e), where they are very close. In Fig. (d), the diagram indicates that no field is present. In Fig. (f), ⊗\otimes denotes a field directed along the −x-x axis, and ⊙\odot denotes a field directed along +x+x axis.

Native candidate (a), all four corner labels and complete electric-field pattern; native caption retained in pixels.
Native candidate (b), closed electric-field loops, all ABCD labels and native caption.
Native candidate (c), all near-touching field lines and ABCD labels with native caption.
Native candidate (d), no field, all ABCD labels and native caption.
Native candidate (e), all fine field lines, ABCD labels and native caption.
Native candidate (f), every circled dot/cross, ABCD labels and native caption.

Отговори

Решение

Теми и трудност

Оценена трудност: 3/5.

Електричество · Електростатика · Електрично поле

Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка

Оригинал в Архива: INPhO2026-Question.pdf · официални решения: INPhO2026-Solution.pdf