Consider a long uniformly charged cylinder having constant volume charge | PGMN Solutions скачать в хорошем качестве

Consider a long uniformly charged cylinder having constant volume charge | PGMN Solutions

Consider a long uniformly charged cylinder having constant volume charge density ' 𝜆 ' and radius ' 𝑅 '. A Gaussian surface is in the form of a cylinder of radius ' 𝑟 ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder (rR). electric field is directly proportional to (A) 𝑟^(−1) (B) 𝑟 (C) r^2 (D) 𝑟^(−2) ✅ Step-by-Step Theoretical Explanation 🚀 📌 Chapter: Electrostatics 📌 Topic: Electric Field Inside a Uniformly Charged Cylinder 🔹 Step 1: Understanding Gauss’s Law – It states that the total electric flux through a closed surface depends on the charge enclosed within that surface. 🔹 Step 2: Choosing a Gaussian Surface – To find the electric field inside the uniformly charged cylinder, we consider an imaginary cylindrical Gaussian surface of radius 🔹 Step 3: Charge Enclosed – The total charge enclosed within this Gaussian surface is proportional to its volume. Since volume increases with the square of the radius, the enclosed charge also follows this relation. 🔹 Step 4: Electric Field Dependence – The symmetry of the system ensures that the electric field is radially outward and is influenced by the enclosed charge. Applying Gauss’s Law conceptually, we conclude that the electric field inside the cylinder increases directly with distance from the axis. ✅ Final Answer: (B) 🚀 🔥 Pro Tip: Inside a uniformly charged cylinder, the electric field behaves similarly to how force increases with displacement in a stretched spring—it grows linearly with distance from the center! 💡 📽️ Must watch if you're preparing for MHT-CET 2025 Physics. Perfect for concept clarity & revision. Welcome to PGMN Solutions – your go-to channel for MHT CET Physics solutions! 🚀 One Question, One Solution – Every Day! 🚀 📌 Get step-by-step solutions to past MHT CET Physics questions, explained by Mukesh Sir. 📌 Master concepts, improve speed, and ace your MHT CET exam with expert guidance. 📌 All solutions are from previous years and important expected questions. 🔔 Subscribe now for daily updates & never miss a solution! 🌐 Visit www.pgmn.live for more Physics resources, test series, and full courses.