Curl — Study Resources & PYQs
Curl and its physical significance.
- Estimated study time: 30 minutes
Study resources
- Curl, fluid rotation in three dimensions - Khan Academy article (Article) — Curl explained as rotation of a fluid, with the determinant form of the formula. Directly underpins the two curl equations in Maxwell's set.
- Partial derivatives, gradient, divergence, curl - Khan Academy (Video) — Watch these if you can state the definition of curl but cannot compute it quickly - works through several examples step by step.
- AskFilo - Del Operator, Gradient, Divergence, Curl (Solved Problems) (Article) — Explains the del/nabla operator and derives gradient, divergence and curl with solved examples (finding div/curl of a vector field).
- Medium - Gradient, Divergence, Curl: Electromagnetics (Part 1) (Article) — Clear conceptual article explaining the physical meaning of gradient, divergence and curl in the context of electromagnetics.
- Lehman College - Lecture 5: Vector Operators: Grad, Div and Curl (PDF) (Article) — University lecture notes (PDF) deriving grad, div, curl in Cartesian coordinates with worked examples.
- NPTEL EM Theory - Week 4 (magnetic field, divergence and curl of B, Ampere's law) (Article) — Week 4 covers the magnetic field of a steady current and derives Ampere's law from Biot-Savart. The modified form with displacement current comes in Week 5.
- Physical Interpretation of grad, curl, div - University of Alberta (Article) — A concise, exam-friendly writeup of what each operator physically means, including solenoidal and irrotational fields. Good source for the 'physical significance' part of the question, which most stu…
Curl previous year questions
- a) Prove the relations: i) $\nabla\times\vec{E} = -\frac{\partial\vec{B}}{\partial t}$ ii) $\nabla\times\vec{B} = \mu_0\vec{J} + \mu_0\epsilon_0\frac{\partial\…
- (a) What is curl of a vector field? Give its significance. Show that curl of gradient of V is zero. (b) Determine the constant 'a' so that vector field $\vec{A…
- a) Show that curl of a vector Field which can be expressed as gradient of another scalar field vanishes i.e. if $\vec{A} = \vec{\nabla} \varphi$ then $\vec{\na…
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