OPhO 2020 Problem 36 | Flattening the Curve | Magnetic Force Between Curved Current-Carrying Wires

OPhO 2020 – Open Round | Problem 36: Flattening the Curve In today's JeeO Physics Daily Problem Series, we solve a beautiful problem from the Online Physics Olympiad (OPhO) 2020 – Open Round. This problem looks conceptually simple at first: two infinitely long current-carrying wires interact through the magnetic field produced by one wire. But the real challenge is mathematical—the second wire is curved and described by an equation, so calculating the total magnetic force requires combining magnetic force, geometry, calculus and integration. Problem Statement Two infinitely long current carrying wires carry constant current \(i_1\) and \(i_2\) as shown in the diagram. The equations of the wire curvatures are \[ y^2-8x-6y+25=0 \] and \[ x=0. \] The magnitude of force acting on wire 2 due to wire 1 is \[ \frac{\mu_0 i_1 i_2}{\beta}. \] The value of \(\beta\) is to be calculated. The current-carrying wires are rigidly fixed. The units for distances on the graph should be taken in meters. This is a fantastic problem for students preparing for JEE Main, JEE Advanced, Physics Olympiads and INPhO, because it connects electromagnetism with mathematical problem-solving and integration. The original problem appeared as Problem 36, “Flattening the Curve,” in the Online Physics Olympiad 2020 Open Round. Opho 🔥 Concepts Covered Magnetic field due to an infinitely long current-carrying wire Force on a current-carrying wire Force between current-carrying wires Curved current-carrying wire Differential elements of force Coordinate geometry Parabolic curves Definite integration Symmetry and vector components Mathematical physics problem solving If you enjoy challenging Physics problems that go beyond routine JEE applications, subscribe to JeeO Physics and follow the Daily Problem Series. 🔎 SEO Keywords OPhO 2020 Problem 36, Online Physics Olympiad 2020, OPhO 2020 Physics, Flattening the Curve Physics, magnetic force between current carrying wires, force between curved wires, magnetic force curved wire, current carrying wire problem, magnetic field due to infinite wire, JEE Advanced Physics, JEE Main Physics, Physics Olympiad problems, INPhO Physics, Olympiad Physics problems, difficult magnetism problems, magnetism and integration, magnetic force integration, current carrying wire JEE Advanced, JeeO Physics 🏷️ YouTube Tags OPhO 2020, Online Physics Olympiad 2020, OPhO 2020 Problem 36, Flattening the Curve, OPhO Problem 36, Physics Olympiad, Physics Olympiad Problems, Olympiad Physics, JEE Advanced Physics, JEE Main Physics, JEE Physics, Magnetism JEE Advanced, Magnetic Force, Magnetic Field, Current Carrying Wire, Force Between Current Carrying Wires, Curved Current Carrying Wire, Magnetic Force Between Wires, Magnetic Force Integration, Physics Integration Problems, INPhO, Indian Physics Olympiad, Physics Problem Solving, JeeO Physics #️⃣ Hashtags #OPhO2020 #PhysicsOlympiad #JEEAdvanced #JEEMains #Magnetism #Physics #INPhO #OlympiadPhysics #JeeOPhysics