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`Magnetic Force in Moving Metal BarβElectricity in Moving Metal BarβElectric and Magnetic ForcesβRelativity of Electric and Magnetic FieldsβSource and Reference`

Magnetic Force in Moving Metal Bar

By pulling a metal bar through a magnetic field at constant speed π£, electron charges inside the metal bar are moved by magnetic force πΉ=(-π)π£Γπ΅ to build up on one side. The electron current flows towards bottom until net force acting on electron is balanced by charge build up, that is πΉnet=0. ```πΉnet=ππΈ+ππ£Γπ΅=0 β|πΈ|=|π£||π΅| in steady state equilibrium```

Electricity in Moving Metal Bar

By connecting a metal bar to a closed circuit during pulling the metal bar through a magnetic field at constant speed π£, electron charges inside the metal bar are moved by magnetic force along one direction. Since the metal bar is connected to a closed circuit, the current inside the metal bar flows around the closed circuit. The work done by moving the metal bar is ```πΉπΌ=πΌβπΓπ΅=βπΉhandβπΉπΌ=πΌπΏπ΅ Work: π=πΉβπ₯=πΌπΏπ΅βπ₯ Power: π=πβπ‘=πΌπΏπ΅βπ₯βπ‘βπ=πΌπΏπ΅π£ ββ΅emf=|πΈ|πΏ=π£π΅πΏβπ=πΌ(emf) ```

Electric and Magnetic Forces

The electric and magnetic forces are πΉ=ππΈ1=ππ£Γπ΅ The electric field due to 1 on 2 is πΈ1=14ππ0π1π2π
The electric force on 2 due to 1 is πΉ21,π=π2πΈ1=14ππ0π2π1π2πβπΉ21,π=14ππ0π2π2 The magnetic field due to 1 on 2 is π΅1=π04ππ1π£1π2π
The magnetic force on 2 due to 1 is πΉ21,π=π2π£2Γπ΅1=π2π£2π04ππ1π£1π2πβπΉ21,π=π04ππ2π£2π2 The ratio of magnetic force over electric force is πΉ21,ππΉ21,π=π04ππ2π£2π2/14ππ0π2π2=π0π0π£2
Since π0π0=1π2βπΉ21,ππΉ21,π=π£2π2
Therefore πΉπβ€πΉπ

Relativity of Electric and Magnetic Fields

Magnetic field measurement depends on frame of reference. The Lorentz factor πΎ=1β1βπ£2/π2>1
Theory of relativity is the speed of light in vacuum = constant π = 3Γ10^8m/s always constant in every references frame. Space and time warp to preserve the speed of light. That is length contraction πΏobserved=πΏ/πΎ, time dilation π‘observed=πΎ*π‘, mass increase πobserved=πΎ*π. Electric and magnetic field also adjust. Special relativity is wiggy. Since electric and magnetic fields are closely related, they are usually called electromagnetic field. The observed electromagnetic field of a rapidly moving particle is ```πΈβ²π₯=πΈπ₯ πΈβ²π¦=πΎ(πΈπ¦βπ£π΅π§) πΈβ²π§=πΎ(πΈπ§+π£π΅π¦) π΅β²π₯=π΅π₯ π΅β²π¦=πΎ(π΅π¦+π£πΈπ§/π2) π΅β²π§=πΎ(π΅π§βπ£πΈπ¦/π2) ```

Source and Reference

ID: 200101202 Last Updated: 1/12/2020 Revision: 0

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