Motion of Point Charges:
A particle of mass m and charge q moving with speed v in a plane perpendicular to a uniform magnetic field moves in a circular orbit. The period and frequency of this circular motion are independent of the radius of the orbit and of the speed of the particle.
Newton's 2nd law: qvB=m((v^2)/r)
Cyclotron period: T= 2(pi)m/(qB)
Cyclotron Frequency: f= 1/T = (qB)/(2(pi)m)
consists of corssed electric and magnetic fields so that the electric and magnetic forces balance for a partivle moving with speed v.
The mass-to-charge ratio of an ion of known speed can be determined by measuring the radius of the circular path taken by the ion in a known magnetic field.
Magnetic dipole moment: u= NIAn
Torque= t= u x B
Potential energy of a magnetic dipole: U= -u . B
Net force on a current loop in a uniform magnetic field is 0.
Biot Savart Law:
Magnetic field lines: the magnetic field is indicated by lines parallel to B at any point whose density is proportional to the magnitude of N. Magnetic lines do not begin or end at any point in space. Instead, they form continuous loops.
Gauss's Law for magnetism: Net flux= integral over the closed surface( BdA)= 0
Integral over the closed surface (B . dl)= (u_0)I_perm
These are the main and basic laws and concepts of magnetism. Other equations can be derived for different objects with current flowing through them and deriving them helps to gain a better understanding of the relationships between different objects and their magnetic fields when current is induced.