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Content

Eletric Current
 Biot-Savart Law of Current in Wire
 Properties of Biot-Savart Law
 Source and Reference

Eletric Current

Electron current is the current that electrons exit batter at -ve terminal, and enter battery at -ve terminal. Conventional current is the current that fictitous positive charges exit battery at +ve terminal, and enter battery at -ve terminal.

Electron Current 𝑖=𝑛𝐴𝐿𝐿/𝑣=𝑛𝐴𝑣=electronssecond

   Conventional Current 𝐼=|𝑞|𝑛𝐴𝑣=Coulombssecond=Amperes

    where 𝑛=electrons𝑚³= Density of electrons in the wire

    𝐴=[𝑚²]= Cross sectional area of the wire

    𝑣=𝑚𝑠= Average velocity of electrons in the wire.

Biot-Savart Law of Current in Wire

The Biot-Savart Law of Current in Wire is ∆𝐵=𝜇₀4𝜋𝐼∆𝑙×𝑟|𝑟|² The Biot-Savart Law of current in wire can be dervied from Biot-Savart Law of charge particle. The current in the wire can be considered as many point charges in the wire. 𝑄𝑣=𝑁𝑞𝑣=𝑛𝐴∆𝑙𝑞𝑣=𝑞|𝑣|𝑛𝐴∆𝑙=𝐼∆𝑙

Properties of Biot-Savart Law

Magnetic field depends on frame of reference. The velocities of charges must be used the same reference frame as the observer.
Biot-Savart Law is an approximation. The changes of B-field or E-field propagate at speed of light. The law assumes that 𝑣≪𝑐, and the measurement is not taken so quickly.