If I stretch out a solenoid I get a straight wire. Both in solenoid and straight wire moving charges are producing magnetic field then why is magnetic field of a straight wire solenoid and a circular wire different shouldnt it be same in all?
If I stretch out a solenoid I get a straight wire. Both in solenoid and straight wire moving charges are producing magnetic field then why is magnetic field of a straight wire solenoid and a circular wire different shouldnt it be same in all?
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
B⃗ =μ0/4π q (v⃗ × r⃗ )/r^3 at a point with position vector r⃗ 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 B⃗ both=B⃗ loop1+B⃗ 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.
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
B⃗ =μ0/4π q (v⃗ × r⃗ )/r^3at a point with position vector r⃗ 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 B⃗ both=B⃗ loop1+B⃗ 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.
