After reading the title, the first thing which could pop-up in your mind is Magnets. Absolutely valid. Magnets are the most common source of Magnetic fields. It starts from North pole and terminates at South pole. The same field results in the interaction of Magnets.
Just like charges of same sign repel and of opposite sign attract. Likewise, like poles repel and unlike poles attract. So, North-North or South-South will repel while North-South will attract.
But magnets are not the only source of Magnetic field. It can be produced by moving charge as well. Eventually, a current carrying wire will also produce magnetic field (As current is nothing but moving charges)
It is customary to denote magnetic field by 
. Its SI unit is Tesla (T) or 
where Wb is Weber while CGS unit is Gauss
Biot-Savart law: Biot-Savart gave the formula for the magnetic field produced due to the small current carrying element.
![\[d\vec{B}=\frac{\mu_0 i(d\vec{l}\times d\vec{r})}{4\pi r^3}\]](https://i0.wp.com/tutortonight.com/wp-content/ql-cache/quicklatex.com-6a0d99a1d7cd04e4e09913d6c3beb1ac_l3.png?resize=142%2C42&ssl=1 "Rendered by QuickLaTeX.com")
Where, 
is the elemental current carrying wire and 
is the position vector of the point where magnetic field is to be determined.
Another way to write the magnitude of this magnetic field is
![\[dB}=\frac{\mu_0 idlsin\theta}{4\pi r^2}\]](https://i0.wp.com/tutortonight.com/wp-content/ql-cache/quicklatex.com-0bfda161e94781a560af45154250b599_l3.png?resize=123%2C36&ssl=1 "Rendered by QuickLaTeX.com")
Where 
is the permeability of vacuum. Its value is 
Direction: Direction of magnetic field is determined using Right hand palm rule. We stretch our right hand such that thumb is pointing towards current while fingers are towards position vector. Push will give the direction of Magnetic field.
I have talked about this in the below video using examples.
Force on a moving charge inside magnetic field: When a moving charge enters a magnetic field, it experiences (magnetic) force which is given by
![\[F= q(\vec{v}\times \vec{B})\]](https://i0.wp.com/tutortonight.com/wp-content/ql-cache/quicklatex.com-888cabe0ceb95c57cedbd143add71853_l3.png?resize=104%2C23&ssl=1 "Rendered by QuickLaTeX.com")
Or
![\[F= qvBsin\theta\]](https://i0.wp.com/tutortonight.com/wp-content/ql-cache/quicklatex.com-216e19ff1f1000335197a83b188afeb7_l3.png?resize=104%2C16&ssl=1 "Rendered by QuickLaTeX.com")
Since this is a cross product, resultant force will always be perpendicular to both velocity and Magnetic field.
Direction: Direction is given by Right hand thumb rule. Curl the fingers of right hand from velocity to magnetic field. Thumb will point the direction of magnetic force.
Special case: When charge enters perpendicular to the magnetic field, it starts moving in a circle. Why?
Check out this video. I’ve covered some examples as well.
Stay tuned for further blog posts.
Struggling with one of your question? Post it down in the comment section.