# why does adding loops in a straight wire increase the magnetic field?

I have seen heaps of articles about what happens to the coil and the magnetic field but nothing about why exactly the overall magnetic field increases when loops are added to a straight wire to increase magnetic field.

Also why is a magnetic field produced when a current is passed though a straight wire?

Your questions get answered if you realize that magnetic field follows the superposition principle i.e. magnetic field at a certain point due to multiple sources is the vector sum of the magnetic fields at that point due to the individual sources.

Also why is a magnetic field produced when a current is passed though a straight wire?

A magnetic field is produced whenever a charged particle moves, and is given by $$\vec B = \frac{\mu_0}{4\pi} \ q \ \frac{(\vec v \ \times \ \vec r)}{r^3}$$

at a point with position vector $\vec r$ with respect to the charged particle. Thus, we can associate a megnetic field with a moving charge.

Current in a straight wire is really just a bunch of charges moving in a certain direction. As the magnetic field follows superposition principle, we can just take the vector sum of the magnetic fields due to all the individual charges to yield the net magnetic field at that point. Put simply, each moving charge in the current contributes a little bit to the total magnetic field at a point. That's how a current carrying wire makes its magnetic field.

why exactly the overall magnetic field increases when loops are added to a straight wire

The magnetic field of a loop, at certain points, is more than a magnetic field due to a straight wire for the simple reason that (as seen in the equation above) magnetic field decreases with distance from the charges/wire. In a circular loop, all charges flowing are at the same distance from a point on its axis, in contrast to a straight wire where different parts of the wire are at different distances from a given point. Thus a loop, in a way, concentrates the magnetic field which was spread out in the case of a straight wire.

If you have a current carrying loop, it will produce a magnetic field which in turn is a result of the sum of magnetic fields due to the individual charges in motion inside it. Again, as the magnetic field follows superposition principle, if you have another loop next to the first, then the magnetic field at a certain point will be the sum of the magnetic fields due to the individual loops. What this means is that if you calculate the magnetic field a point only due to the first loop, and then only due to the second loop, the total magnetic field in the presence of both the current carrying loops will be given by $\vec B_{both} = \vec B_{loop1} + \vec B_{loop2}$

If these two fields support each other (which they do in your question, as the current in both the loop is in same direction), then surely the magnetic field will be magnified.

Now imagine that the loops are of the same wire coiled twice. That would make no difference in the above conclusions and the magnetic field will increase. Coiling the wire more number of times will thus further increase the magnetic field.

Matter is made of atoms and each atom consists of electrons circulating around the nucleus.These moving electrons constitute electric current at the atomic level.We can assume these currents as small,circular current loops.In magnets,these loops are arranged nearly parallel to each other and have current in the same direction. Let us consider a cross section of a cylindrical bar magnet.At any point inside it ,net current will be zero because currents from adjacent loops cancel each other.But there's a net current along the surface as there's no cancellation of current.Due to the surface current , the magnet is equivalent to a current carrying solenoid and produces a magnetic field. A long straight wire produces magnetic field due to moving electrons.