Magnetic Field Interface Problem — Smart Geometry Method 💡
❓ Question Uniform magnetic fields of different strengths B 1 B_1 B 1 and B 2 B_2 B 2 , both normal to the plane of the paper , exist as shown in the figure. A charged particle of mass m m m and charge q q q , at the interface at an instant, moves into region 2 with velocity v v v and returns to the interface . It then continues to move into region 1 and finally reaches the interface again. What is the displacement of the particle along the interface during this complete motion? 🖼️ Question Image ✍️ Short Solution This is a pure concept-based JEE magnetism problem . No equations of motion — only circular motion + geometry . 🔹 Step 1 — Motion of a charged particle in uniform magnetic field When a charged particle with velocity v v v enters a region with a uniform magnetic field B B B (perpendicular to the velocity): The particle moves in a circular path Radius of circular motion: r = m v q B So in the two regions: r 1 = m v q B 1 , r 2 = m v q B 2...