• Magnetic fields exist around current-carrying wires.
• We're looking at the force between two wires due to their magnetic fields.

• Magnetic Field Pattern around a straight wire - Looks like circles centered on the wire.
• Field Strength B: B =\(\frac {μ0I}{2πr}\)​ (It's a 1/r law, unlike the 1/r² we see elsewhere!)
• Force Between Wires: Using the field from one wire, we can calculate the force on the other.
• Permeability of Free Space (μ0): It's how a vacuum responds to a magnetic field. Its value is 4π ×10⁻⁷ N A^-2.

Real-world Analogy: Think of two people holding magnets. The closer they are, the stronger the pull. Similarly, closer wires with currents feel a stronger force due to their magnetic fields.

• Ampère: Self-taught using dad's library. Studied electrodynamics (now electromagnetism). SI unit of current, the "ampere," is named after him.
• Faraday: Read books while apprenticing as a bookbinder. He confirmed Ampère’s law and created the first electric motor.

Real-world Example: Ampère was like a kid using YouTube tutorials instead of school. And Faraday? He's like someone learning from random library books and making inventions.

• Two wires (X and Y) with currents 8.0A and 3.0A.

• Force on 0.20m of wire X due to Y: 51.5 × 10⁻⁵ N

  a. Force on wire Y due to X: By Newton's 3rd law (action-reaction), it's the same force but in the opposite direction. So, 1.5×10⁻⁵N.

  b. Distance between wires: Using our formula, we find it's 6.4cm.