A long, directly wire carries a present of 2.5 μA. One electron move parallel to the wire v a continuous speed the 3.6x104 m/s at street "d" listed below the wire. What is the magnitude and direction fo the magnetic ar at the location of the electron?
Hi Gnarls (I favored "Crazy," by the way):
The cheat in this sort of problem generally is what they perform not tell you, since it seems choose there might not be sufficient information. The key, though, is in the phrase "parallel to the wire." A charged particle in a ar should normally curve. If that does not, there need to be some other pressure on it balancing the end the magnetic force. In this case, the is the force of gravity on the electron.
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Therefore, the magnetic pressure on the electron requirements to it is in "up" (i.e. Toward the wire, due to the fact that the electron is stated to be below). And also its magnitude need to equal mg because that the electron (whose mass can be quickly looked up).
Since the electron is traveling parallel come the wire, and also the magnetic field of the cable exists in concentric circles about the wire, the particle need to be travel perpendicular come the field as it move parallel to the cable (by geometry). Therefore, the magnetic force on the is qvB. Because v is given and the fee q that the electron is likewise a generally known value (easy come look up), this allows solving for the stamin of the magnetic field at the electron"s position.
There is a conventional formula for the magnetic ar a perpendicular distance r native a long, directly wire:
B = μoi/2πr, whereby r is the perpendicular distance and i is the existing (and μo is (magnetic) permeability (of complimentary space), one more universal constant)
This will enable you to settle for r, the distance from the wire.
The direction of the existing is a choice between "in the very same direction as the particle" and also "opposite the direction that the particle." You have to use the right-hand dominion for the force on a moving charge to identify the direction that the ar to gain an upward force on the electron below the wire (remember that the electron has a an adverse electric charge). One you determine the direction the the field listed below the wire, then recognize (by a various right-hand rule) the direction the existing needs to go in the cable to gain the magnetic field in the suitable direction listed below it.
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For comparison, I got the street to it is in 323 m and also the direction of the existing to be opposite the direction the the electron"s travel (I carry out not make any guarantees around the correctness of this results, yet I confirm my occupational a pair times and got the exact same answer; if ns think of one error later, I will repost).