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Many Class 12 students know the final formula of a derivation and still lose marks on it. The reason is simple: CBSE does not mark the last line. It marks the steps that lead to it. This post shows how the marks are split, gives a five-part structure you can use for any derivation, and works through one in full.
How does CBSE mark a derivation?
The CBSE Class 12 Physics sample question paper for 2026-27 has 33 questions in five sections, with 3-mark questions in Section C and 5-mark questions in Section E. Derivations appear in both: Question 26 asks you to derive Snell's law from Huygens' wave theory, and one option in Question 31 asks you to show that the electric field equals the negative of the potential gradient.
The marking scheme for the same paper shows how those marks are earned. For the potential gradient derivation, the 3 marks come in six half-mark pieces: setting up a small displacement of a test charge, the force qE, the work done, the definition of potential difference as work per unit charge, combining them to get dV = −E dr, and the final statement. The Snell's law answer has a mark for stating Huygens' principle, a mark for the geometry linking sin i and sin r to the two speeds, and a mark for reaching Snell's law and the experimentally verified prediction.
So a student who writes only "E = −dV/dr" gets a fraction of the marks. A student who sets up the problem and makes a slip near the end keeps most of them. The Physics curriculum for 2026-27 also says about 32% of theory marks test applying and about 30% test analysing, evaluating and creating, so derivations are one of the few places where steady, careful writing alone earns marks. Check the sample paper for your own year, since CBSE publishes a new one each session.
What structure should every derivation follow?
Use the same five parts every time.
State the principle. One line: "Gauss's law: the total flux through a closed surface is q/ε₀."
Draw and label the diagram. Show the surface, the field direction and every length you will use.
Define symbols and assumptions. "Let λ be the charge per unit length. The wire is infinitely long, so the field is radial."
Write one idea per line. Each line should follow from the one before, with a few words saying why.
Box the result and check it. State it in words too, and check its units or a limiting case.
Worked example: field of an infinitely long charged wire
Principle. Gauss's law: ∮E·dA = q_enclosed/ε₀.
Set-up. An infinitely long straight wire carries uniform charge λ per unit length. By symmetry, the field is radial and has the same magnitude at every point a distance r from the wire. Choose a Gaussian cylinder of radius r and length l, coaxial with the wire. (Draw it: wire along the axis, field arrows pointing outward, flat ends marked.)
Steps.
On the two flat ends, E is parallel to the surface, so the flux through them is zero.
On the curved surface, E is perpendicular to the surface and constant in magnitude, so the flux is E × 2πrl.
Total flux = E × 2πrl.
Charge enclosed = λl.
By Gauss's law, E × 2πrl = λl/ε₀.
So E = λ/(2πε₀r), directed radially outward for positive λ.
Check. The field falls as 1/r, more slowly than the 1/r² of a point charge, which makes sense for a charge spread along a line. Units: (C/m) ÷ (C²N⁻¹m⁻² × m) = N/C. Our guide on dimensional analysis as a 30-second check shows how to run that test quickly.
Which mistakes cost the most marks?
No diagram, or an unlabelled one. In this example, the diagram is what justifies "zero flux through the ends". Our post on drawing the diagram first explains why it also helps you think.
Symbols that appear from nowhere. If l or λ is never defined, the examiner cannot follow the step.
Skipping the symmetry argument. "E is constant on the curved surface" needs a reason.
Answering only half the question. Question 26 in the sample paper also asks which prediction of wave theory was later verified. Underline every part of the question before you start.
A final result with no direction or units. Fields are vectors. Say which way they point.
How should you practise derivations?
Reading a derivation in the textbook feels like learning it, but it is not the same as producing it. In an experiment by Roediger and Karpicke (2006), students who practised recalling a passage remembered more of it two days and a week later than students who reread it, even though rereading made students more confident. Writing a derivation from a blank page is that kind of recall.
One derivation a day. Pick it from the syllabus list, close the book and write it in the five-part structure.
Mark yourself in half-marks. Compare with the NCERT text and the CBSE marking scheme. Circle any step you skipped.
Redo the circled ones two days later, then again a week later.
Time the long ones. A 5-mark question should take you about as long as its share of the paper allows.
If you keep getting stuck at the same step, the gap is usually a concept, not memory. Fermi's AI tutor writes on a board, draws the figure and checks understanding as it goes, so you can rebuild the reasoning behind the step instead of memorising it. To fit derivations into the rest of your revision, see our 8-week Class 12 board revision plan.
Tonight, write the charged-wire derivation from memory, then mark it against the six steps above.
