What Is a Magnetic Field?

By now, you can probably see the pattern.

Unfortunately, it cannot be that simple. Why, you may ask? It is because, as far as we know, there is no such thing as a magnetic monopole. All of our observations of the universe so far show that magnetic poles always come in pairs. Moreover, magnetic forces behave differently from gravitational and electrostatic forces; for example, a stationary particle will not experience a magnetic force.

Scientists working with magnets noticed the following properties about the magnetic force: (1) it was proportional to the electric charge, (2) it was proportional to the speed of the particle, and (3) it was always perpendicular to the velocity of the particle. Thus, the magnetic field was defined as follows:

Let a particle have charge $q$ and velocity $\vec{v}$. Suppose that the magnetic force acting on the particle is $\vec{F}$. Then the magnetic field $\vec{B}$ is defined as the unique vector that will satisfy the equation: $$\vec{F}=q(\vec{v}\times\vec{B})$$

In simple language the magnetic field of a magnet is circular area under which the power of the magnetic field can be felt.