Emf can be induced in a conductor through magnetic flux changes in several cool ways

• Move a wire in a consistent magnetic field (Imagine sliding on an ice rink! 🛷)
• Keep the wire still, but let the magnetic field strength change (Like volume control on your speakers 🎚️)
• Change the size or direction of a coil in a stable magnetic field (Transform! 🤖)

Case 1 - Wire Moves in a Field

• Like a rod rolling on parallel rails.
• Formula Magic: 𝜀 = BvL (when the wire moves 90° to field lines)
  • B = magnetic field, v = speed, L = length of the rod
• Not 90°? Just use the field component that is!

💡Think of it like this: Trying to walk straight into the wind is harder than walking diagonally to it! 🌬️
 

Case 2 - The Dancing Coil

• If a coil moves between areas of equal magnetic fields, no emf gets induced (they cancel each other out).
• Faraday had this wacky idea: think of magnetic field lines like "tubes of force" (Like invisible spaghetti! 🍝).
• When a coil flips 180°, the field lines seem to reverse, so the flux change is basically doubled!
  • Emf induced = (2NΦ) ÷ time taken
• For rotating coils, the emf is like a DJ's beats, going up and down, creating what we know as alternating current!

Real-world example: This is how generators in power plants work! Like a DJ spinning records, but for electricity. 🎧

Case 3 - The Sneaky Magnetic Field

• What if the field changes around a stationary coil?
  • When the field goes from zero, it's like field lines sneaking into a party (the coil) they weren't invited to.
  • Formula Magic: 𝜀 = -NAΔB ÷ Δt
• Think of two coils facing each other; one with a galvanometer, and the other with a cell and a switch. Closing and opening the switch can change the emf!

For Geeks: If flux linkage vs time was a mountain ⛰️, the induced emf is like its steepness!

• Problem 3: For a coil with 500 turns and flux change, the emf induced = 250V.
• Problem 4: Two objects dropped in a tube
  • Aluminium cylinder (non-magnetic) takes ~0.55s.
  • Magnet takes longer (5s) because it's kinda arguing with the tube's own magnetic field as it goes down (Lenz's law).