Andre-Marie Ampere is known for the electromagnetism concept that gives the relationship between the electric current and magnetic fields. There are many formulas in magnetism. Some of them are:

Magnetic force that acts on a charge q is given as,
F = qvB sin $\theta$.
Where,
F is the force,
q is the charge,
v is the velocity,
B is the magnetic field,
$\theta$ is the angle between B and v.

Force that acts on a wire in a magnetic field is given as,
F = BIL sin $\theta$.
Where,
F is the force,
B is the magnetic field,
I is current flow,
L is length,
$\theta$ is the angle between B and v.

Torque on a rectangular loop is given as,
$\tau$ = NBIA sin $\theta$.

Where,
N is the number of turns,
B is a magnetic field,
I is current in amperes,
A is area,
$\theta$ is the angle between B and v.

Charged particle in a magnetic field is given as,
r = $\frac{mv}{qB}$.
Where,
r is the radius of the path,
m is the mass,
v is the velocity,
q is the charge,
B is the magnetic field.

Lets see some magnetism examples given below:

Question 1: The charged particle experiences a magnetic field of 8 $\times$ 10$^{-5}$ N/Amps.m has a charge of 100 C having velocities of 320 m/s moves with an angle of 20o. Calculate the force due to the magnetic field.
Solution:
Given:
Magnetic field B = 8 $\times$ 10-5 N/Amps.m,
Charge q = 100 C,
velocity v = 320 m/s,
angle $\theta$ = 20$^{\circ}$

The force experienced in a magnetic field is given by,
F = q v B sin $\theta$
F = 100 C $\times$ 320 m/s $\times$ 8 $\times$ 10$^{-5}$ N/Amps.m $\times$ sin 20o
F = 0.87 N

Therefore, the force due to magnetic field is 0.87 N.

Question 2: The magnetic field is applied on the metal wire of length 200 m having a magnetic field of 20 $\times$ 10$^{-6}$ Tesla and a current of 10 Amperes at an angle 18o. Calculate the force.
Solution:
Given:
Magnetic field B = 20 $\times$ 10-6 N/Amps.m,
current I = 10 Amperes,
length L = 200 m

The force experienced in a magnetic field is given by,
F = BIL sin $\theta$
F = 20 $\times$ 10$^{-6}$ N/Amps.m $\times$ 10 A $\times$ 200 m $\times$ sin 18o
F = 0.0123 N.

Therefore, force due to magnetic field is 0.0123 N.