Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
184_notes:magnetic_field [2017/11/30 00:12] – dmcpadden | 184_notes:magnetic_field [2021/07/06 17:31] (current) – bartonmo | ||
---|---|---|---|
Line 1: | Line 1: | ||
Chapters 17 and 20 of Matter and Interactions (4th edition) | Chapters 17 and 20 of Matter and Interactions (4th edition) | ||
+ | |||
+ | / | ||
+ | |||
+ | [[184_notes: | ||
===== The Magnetic Field ===== | ===== The Magnetic Field ===== | ||
Line 5: | Line 9: | ||
When charges are at rest, they [[184_notes: | When charges are at rest, they [[184_notes: | ||
- | ==== Model of a moving point charge ==== | + | {{youtube> |
+ | ===== Model of a moving point charge ===== | ||
+ | [{{ 184_notes: | ||
Our introduction to the magnetic field started with [[184_notes: | Our introduction to the magnetic field started with [[184_notes: | ||
Line 12: | Line 18: | ||
where the vector →r is still the separation vector between the location of the moving charge at a given time and the observation location at the same time -- assuming that the charge is moving much more slowly than the speed of light. Again, we cannot derive this equation, it is a model of the point charge magnetic field that fits the data/ | where the vector →r is still the separation vector between the location of the moving charge at a given time and the observation location at the same time -- assuming that the charge is moving much more slowly than the speed of light. Again, we cannot derive this equation, it is a model of the point charge magnetic field that fits the data/ | ||
+ | |||
+ | [{{184_notes: | ||
If another moving charge is brought into the scene, it will interact with the first moving charge through the magnetic field that the first charge generates. (It will also experience the electric force, but we often limit our discussion at first to the isolated magnetic interaction.) This push or pull that the new moving charge experiences is directly related to the cross product of the velocity of that charge and the magnetic field of the source charge. This [[184_notes: | If another moving charge is brought into the scene, it will interact with the first moving charge through the magnetic field that the first charge generates. (It will also experience the electric force, but we often limit our discussion at first to the isolated magnetic interaction.) This push or pull that the new moving charge experiences is directly related to the cross product of the velocity of that charge and the magnetic field of the source charge. This [[184_notes: | ||
Line 19: | Line 27: | ||
The direction of the force is determined by the [[184_notes: | The direction of the force is determined by the [[184_notes: | ||
- | ==== Collections of moving charges ==== | + | ===== Collections of moving charges ===== |
+ | [{{ 184_notes: | ||
A single moving charge is certainly not the only kind of situation that we encounter. In fact, it's quite often that a collection of charges are moving -- forming a current. This collection of moving charges or really [[184_notes: | A single moving charge is certainly not the only kind of situation that we encounter. In fact, it's quite often that a collection of charges are moving -- forming a current. This collection of moving charges or really [[184_notes: | ||
Line 31: | Line 40: | ||
→Bnet=∫d→B=∫μ04πId→l׈rr2 | →Bnet=∫d→B=∫μ04πId→l׈rr2 | ||
- | We can use this integration technique analytically and computationally to find the magnetic field produce by a distribution of current. | + | We can use this integration technique analytically and computationally to find the magnetic field produce by a distribution of current |
- | + | ||
- | ==== Effects and Applications ==== | + | |
+ | ===== Effects and Applications ===== | ||
The fact that moving charges generate magnetic fields, that they superpose, and that other moving charges experience magnetic forces in the presence of a magnetic field result in a number of different magnetic phenomenon. Some are quite practical. Some of the most important ones are discussed below: | The fact that moving charges generate magnetic fields, that they superpose, and that other moving charges experience magnetic forces in the presence of a magnetic field result in a number of different magnetic phenomenon. Some are quite practical. Some of the most important ones are discussed below: | ||
+ | [{{ 184_notes: | ||
- | === Current-carrying wires === | + | ===== Current-carrying wires ===== |
- | Wires that carry current will produce magnetic fields that circulate around them. This stems from the superposed magnetic fields from all the little charges moving in the wire. This can be quite important because those magnetic fields might disturb other sensitive electronics in a particular electronic device or experiment. Moreover, pairs of current carrying wires can exert forces on each other (attractive or repulsive) causing physical stress on the wires or other components. | + | Wires that carry current will produce magnetic fields that circulate around them. This stems from the superposed magnetic fields from all the little charges moving in the wire. This can be quite important because those magnetic fields might disturb other sensitive electronics in a particular electronic device or experiment. Moreover, |
- | === Curved motion === | + | ===== Curved motion ===== |
+ | [{{ 184_notes: | ||
- | Magnetic fields cannot change the kinetic energy of charged particles. This is because the magnetic force acting on the particle is always perpendicular to motion of the particle. So magnetic fields can change the trajectory of a particle, but are not able to speed up or slow down the motion of the particle. As a result a particle moving in a uniform magnetic field subject to no other forces will execute uniform circular motion. The direction of the orbit (clockwise vs counterclockwise) will depend on the sign of the charge, the direction of the velocity, and the direction of the magnetic field. | + | Magnetic fields |
- | This is a very useful result | + | This is a very useful result in cyclotron accelerators |
- | === Changing magnetic fields === | + | ===== Changing magnetic fields |
Much of our study of magnetic fields focused on fields due to steady currents, that is, magnetic fields that didn't change with time. The field was produced a steady stream of charge carriers that we modeled as moving with the same speed and direction. This doesn' | Much of our study of magnetic fields focused on fields due to steady currents, that is, magnetic fields that didn't change with time. The field was produced a steady stream of charge carriers that we modeled as moving with the same speed and direction. This doesn' | ||
- | In the case of a current that changes in time, we produce a time-varying magnetic field. This kind of magnetic field is observed to generate a curly electric field. This electric field is not due to static charges and, hence, we called it a non-Coulombic electric field. This field has very practical uses, in particular, recent advances in inductive charging (also called wireless charging) uses this approach. A coil produces a magnetic field that varies with time which is used to drive a current in another coil that charges a device without physical contact. | + | In the case of a [[184_notes: |