Faraday’s Law of Induction Review Faraday’s Law of Induction

Faraday’s Law The fourth Maxwell Equation Calculates induced emf due to changing magnetic flux

Magnetic Flux ΦB = BA ΦB= BAcos(θ) ΦB: magnetic flux (Wb) B: magnetic field (T) A: area (m2) θ : angle between the magnetic field and a vector which is normal to the area

Unit of Magnetic Flux Weber (Wb) 1 Wb = 1 Tm2

E = -dΦB/dt Faraday’s Law E : induced potential (V) ΦB: magnetic flux (Wb) t: time (s)

Ways to Change Flux ΦB = BAcos(θ) a) Change B b) Change A c) Change θ

E = B L v Motional emf L: length of bar or wire E : induced potential L: length of bar or wire V: speed of bar or wire

Lenz’s Law When the magnetic flux is changing, current will flow so as to oppose the change in flux.

Induced E-Field Caused by changing magnetic flux Does not arise from charge Causes induced potential Circular; loopy Non-conservative

Faraday’s Law E = -dΦB/dt E = ∫ Eds ∫ Eds= -dΦB/dt

Betatron: accelerates electrons by changing magnetic flux

Gauss’ Law of Electricity

Gauss’ Law of Magnetism

Faraday’s Law of Induction

Ampere’s Law

Ampere-Maxwell Law

Inductor A coil in a circuit. Resists change in current with an induced potential. Stores energy in a magnetic field.

Inductor, L L When switch is closed, EL opposes emf of cell. EL i E

Inductor, L L e i When switch is opened, EL supports emf of cell. EL

Inductance EL = -L di/dt EL: potential across inductor L: inductance in Henrys i: current in amperes t: time in seconds

Inductance, in general EL = -Nd ΦB/dt Ldi = NdΦB Li = NΦB EL = -Ldi/dt EL = -Nd ΦB/dt Ldi = NdΦB Li = NΦB true for all inductors

Inductance, in solenoids Li = NΦB N = nl ΦB = BA = n μo i Li = n l (n μo i) A L = n2 l μoA

Inductance, in solenoids with paramagnetic filings L = n2 l μoA κB

The LR Circuit E - EL - VR = 0 E - Ldi/dt - iR i = imax(1 - e-t/τ)

The LR Circuit-continued V 0 = EL + V 0 = -Ldi/dt + iR i = imax(e-t/τ) τ = L/R t i

Energy stored in Inductor UB = ½ L i2 UB : energy stored in magnetic field L: inductance in Henrys i: current in amperes

Radius of loop: 16 cm resistance: 8.5 Ω 1.0 B (T) 0.5 2 4 t (s) 6 8