Author Capstone Axis

Torque on a Current Loop  🔄 1 ️⃣ Rectangular loop in a uniform magnetic field Imagine a rectangular coil of area \(A = ab\) carrying a steady current \(I\) and sitting in a region where the magnetic field \(\mathbf{B}\) is perfectly uniform. Two opposite sides feel no push, while the other two experience equal and opposite […]

Moving-Coil Galvanometer (MCG) 🧲 Why we love it 🤔 Need to know if I really flows or how big the voltage drop is? The MCG turns invisible currents into visible twists of a pointer. Simple, clever, and perfect for lab work! :contentReference[oaicite:0]{index=0} Construction 🛠️ A light rectangular coil with N turns can spin freely about

🧲 The Solenoid — Your Friendly Guide 1️⃣ Meet the Solenoid A long solenoid has many closely packed helical turns of insulated wire. Because its length h is much larger than its radius, each turn behaves like a tiny circular loop, and their magnetic fields add up neatly. 🌀 Inside the solenoid, the field points

🚀 Force Between Two Parallel Currents Two long, straight conductors a and b carry steady currents \(I_a\) and \(I_b\) and are separated by a distance \(d\). Each current creates a magnetic field that reaches the other wire and pushes or pulls on it.💡 1 🔧 Magnetic field from one wire For wire a, the field at

Motion in a Magnetic Field 🚀 1. Why the Path Bends but the Speed Stays the Same 🔄 When a charge zips through a magnetic field, the magnetic force always acts sideways to its motion, so it never does work. Speed stays constant while only direction changes — unlike an electric field, which can speed

Magnetic Field Due to a Current Element – Biot-Savart Law 🧲 Every magnetic field you ever meet comes from moving charge – either a flowing current or the tiny “built-in” currents inside particles. The Biot-Savart law tells you exactly how a short piece of current-carrying wire creates that field. 1. Vector Form (the whole story)

Magnetic Field on the Axis of a Circular Current Loop 🔄 The setup is a loop of radius R lying in the y-z plane with its center at the origin and current I flowing counter-clockwise (when viewed from +x). We want the field at a point P on the axis, a distance x from the center. 🎯:contentReference[oaicite:0]{index=0}

🚀 Ampere’s Circuital Law 1. What the law says Curl your right-hand fingers around any closed path that loops around a current. The path integral of the tangential magnetic field along that loop equals the permeability of free space times the total current passing through the surface it bounds: \( \displaystyle \oint \mathbf{B}\!\cdot\!d\mathbf{l}= \mu_0 I

Moving Charges & Magnetism 🔄🧲 1 — Discovery: Electricity meets Magnetism ⚡➕🧲 Hans Christian Oersted (1820) noticed that a compass needle sitting near a straight wire swung sideways the instant current flowed. The needle lined up tangentially to a circle centred on the wire, proving that a current makes its own magnetic field around it :contentReference[oaicite:0]{index=0}.

Magnetic Force 🤔 4.2.1 Sources and Fields Just like a charge Q creates an electric field \( \mathbf E \), a moving charge (or current) produces a magnetic field \( \mathbf B \) 🧲:contentReference[oaicite:0]{index=0}. Both fields are vectors defined at every point in space and obey the superposition principle—add them tip-to-tail to find the net