Rucete ✏ AP Physics 2 In a Nutshell
3. Magnetism and Electromagnetism
This chapter introduces magnetic fields, magnetic forces, electromagnetism, induction, Faraday’s law, and Lenz’s law. It explains how moving charges create magnetic fields and how magnetic fields interact with currents and moving charges.
Magnetic Fields and Forces
• Magnetic fields (B-fields) are created by moving charges.
• Magnetic forces act only on moving charges, not static ones.
• Magnetic field lines emerge from north poles and enter south poles, forming closed loops.
• No magnetic monopoles have been found — poles always come in pairs.
• Ferromagnetic materials (iron, cobalt, nickel) have high permeability and can be strongly magnetized.
Magnetic Force on a Moving Charge
• Force on a moving charge: F = Bqv sin(θ)
• Force is maximum when velocity is perpendicular to B-field; zero when parallel.
• Right-hand rule: fingers in B direction, thumb in v direction, palm faces force direction (positive charges; reverse for negative).
• Magnetic force acts perpendicular to velocity, causing circular motion (centripetal force).
Magnetic Fields Due to Currents in Wires
Straight Wire
• Magnetic field around a straight current-carrying wire forms concentric circles.
• Strength: B = (μ₀I)/(2πr)
• Right-hand rule: thumb points in current direction, fingers curl around wire in B direction.
Loop of Wire
• Magnetic field at center strengthens with more turns: B = (μ₀IN)/(2r)
• Field lines are stronger inside the loop, similar to a bar magnet.
Solenoid
• Wire coil stretched into a cylinder.
• Magnetic field inside is uniform: B = μ₀nI (n = number of turns per length)
• Right-hand rule: curl fingers with current, thumb points along magnetic field inside solenoid.
Magnetic Force Between Two Wires
• Two parallel currents attract if they flow in the same direction, repel if opposite.
• Force per unit length between two wires: F/L = (μ₀I₁I₂)/(2πr)
• Basis for the definition of the ampere (unit of current).
Induced Motional EMF in a Wire
• A conductor moving through a magnetic field experiences an induced emf: ε = Blv
• l = length of conductor inside the field, v = speed perpendicular to B.
• Electrons accumulate on one end, creating a potential difference.
• Induced current direction follows the right-hand rule (force on positive charges).
Magnetic Flux and Faraday’s Law
• Magnetic flux (Φ): Φ = B·A·cos(θ)
• Measures how much magnetic field passes through an area.
• Faraday’s Law: ε = –ΔΦ/Δt
• A changing magnetic flux induces an emf and, hence, a current.
• Lenz’s Law: induced current opposes the change in magnetic flux (negative sign in Faraday’s law).
Applications
• Electric generators convert mechanical rotation into electricity by rotating coils in magnetic fields.
• Transformers step voltage up or down by changing magnetic flux through coils.
In a Nutshell
Magnetism involves forces on moving charges and currents, generated by and producing magnetic fields. Electromagnetism connects electricity and magnetism through Faraday’s and Lenz’s laws. Understanding these principles is key to explaining technologies like motors, generators, and transformers, and fundamental to modern electrical engineering.