Magnetic Force

For an electron charge −𝑒, the magnetic force on a moving electron is in opposite direction to the direction of the cross product 𝑣×𝐵

Motion in a Magnetic Field

In a large area with constant 𝐵⊥𝑣. 𝑑𝑝𝑑𝑡=𝑞𝑣𝐵 By Biot-Savart law of point 𝐵=𝜇₀4𝜋𝑞𝑣×𝑟|𝑟|² and Biot-Savart law of current in a wire 𝐵=𝜇₀4𝜋𝐼∆𝑙×𝑟|𝑟|²

Magnetic Force in a Wire

The magnetic force due to point charge is ∆𝐹_mag=𝑞𝑣×𝐵 and magnetic force due to current in a wire is 𝐹_mag=𝐼∆𝑙×𝐵

Magnetic Force between Parallel Wires

When currents flow in two paralle wire are in same direction, two parallel wires attract each other. When currents flow in two paralle wire are in opposite direction, two parallel wires repel each other

Hall Effect

By measuring the Hall effect for a particular material, the sign of the moving particles that make up the current can be determined. Why would it be anything other than electrons, negative charges. Semiconductors: sometimes currents is carried by electrons, but sometimes it is carried by the holes. In semiconductors, holes, missing electrons, in the electron sea behave like positive charges. When electron current flows through a metal bar under a magnetic field, all moving electrons will be pushed to one side near the bottom. Negative charges are built up one side and expose atomic cores at the other side near the top. In other words, a polarization is built up on the bar by stucking electrons on one side. The electron current will move straight forward again when the gathered charges on the bottom are strong enough to prevent electrons from getting defected by balancing the magnetic force. A voltage difference ∆𝑉 is induced in the metal bar. Similarly, when conventional current of holes flows through a material bar under a magnetic field, all moving holes will be pushed to one side near the bottom. Positive holes are built up on one side and expose negative charges at the other side near the top. In other words, a polarization is built up on the bar by stucking hole on one side. The positive hole current will move straight forward again when the gathered holes on the bottom are strong enough to prevent holes from getting defected by balancing the magnetic force. A hall voltage ∆𝑉 is induced in the material bar. The hall voltage due to holes is opposite to the voltage due to electrons.

Source and Reference

https://www.youtube.com/watch?v=P-5wV6rt_Aw&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=19