Magnetic Field and its Effects?

📌 CONCEPT: When a bar magnet is placed inside a hollow copper tube, an electromotive force (EMF) is induced in the copper tube due to the changing magnetic flux, as the tube is rotated slowly around its axis while the magnet is stationary.

📐 RULE / FORMULA: The induced EMF is given by Faraday's law of electromagnetic induction, which states that the magnitude of induced EMF is equal to the rate of change of magnetic flux through the coil. The equation is E = -N(dΦ/dt), where E is the induced EMF, N is the number of turns of the coil, and dΦ/dt is the rate of change of magnetic flux.

💡 WORKED EXAMPLE: Consider a hollow copper tube of 50 turns with a radius of 0.1 m, rotating at an angular speed of 10 rad/s. The magnetic field of the bar magnet is 0.5 T. Using Faraday's law, we can calculate the induced EMF in the tube: E = -N(dΦ/dt) = -50(π(0.1)^2)(0.5)(10) = -1.25 V.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the induced EMF, which is opposite to the direction of the change in magnetic flux, as given by Lenz's law.