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Energy Density of Electric Field
 Magnetic Field
 Eartg's Magnetic Field
 Biot-Savart Law of a Point Charge
 Source and Reference

Energy Density of Electric Field

Electric field has energy associated with its existence. image If one charged plate in the capacitor is fixed, an another charged plate is moved due to the induced electric field. Word done due to the fixed plate is. 𝐸tot=πœŽπœ€0=π‘„π΄πœ€0⇒𝐸fix=𝜎2πœ€0=𝑄2π΄πœ€0⇒𝑄=𝐸totπ΄πœ€0=2𝐸fixπ΄πœ€0 π‘Š=βˆ«πΉβˆ™π‘‘π‘Ÿ=βˆ«π‘žπΈβˆ™π‘‘π‘Ÿ=βˆ«π‘„π‘„2π΄πœ€0π‘₯βˆ™π‘‘π‘₯=𝑄22π΄πœ€0π‘ βˆ«0𝑑π‘₯=𝑄2𝑠2π΄πœ€0  =𝐸tot𝑄𝑠2=12πœ€0𝐸2tot𝑠𝐴 β‡’π‘Šπ‘ π΄=12πœ€0𝐸2tot=π‘ˆπ‘‰π‘œπ‘™= Energy Density of Electric Field

Magnetic Field

Moving charged particles make a magnetic field, which is different from an electric field. The needle of a magnetic compass aligns with the direction of the net magnetic field at its location. A current is a continuous flow of charge. Electron current is a number of electrons per second entering a section of a conductor. Conventional current (Coulombs/second) is opposite in direction to the electron current, and is assumed to be due to positively charged particles. The superposition principle can be applied to calculate the expected magnetic field from current-carrying wires in various configurations. A current-carrying loop is a magnetic dipole. A bar magnet is also a magnetic dipole. Even a single atom can be a magnetic dipole.

Eartg's Magnetic Field

|𝐡Earth|~20 microTesla=2Γ—10βˆ’5𝑇; typical 𝑁𝑑 Magnet~1𝑇. The axis of Rarth magnet field is tilted by 11.3 degrees from the Earth rotational axis. In fact, magnet field sign reversals happens throughout Earth's history.

Biot-Savart Law of a Point Charge

image Moving charges create a magnetic field. 𝐡=πœ‡04πœ‹π‘žπ‘£Γ—π‘Ÿ|π‘Ÿ|2
π‘ž = charge; 𝑣 = velocity of charge; π‘Ÿ = observation point (charge at origin);
πœ‡04πœ‹β‰‘1Γ—10βˆ’7Teslaβˆ™mβˆ™sCoulomb
The cross product follows the right hand rule. The resulting vector has the magnitude: |π‘£Γ—π‘Ÿ|=|𝑣||π‘Ÿ|sin πœƒ

Source and Reference

https://www.youtube.com/watch?v=ovlGI02gMx4&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=11


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ID: 191201102 Last Updated: 11/12/2019 Revision: 0

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