What is the magnetic field generated by these two particle beams?

AI Thread Summary
The discussion revolves around the magnetic field generated by two parallel beams of charged particles, one positively charged and the other negatively charged, moving in opposite directions. Participants explore the relationship between moving charges and magnetic fields, referencing Biot-Savart's Law and Ampere's circuital law. They clarify that a moving charge can be treated similarly to a current, allowing for the application of these laws to the particle beams. The magnetic field is expected to vary radially from each beam, and the principle of superposition can be used to analyze the overall field. The conversation emphasizes the importance of understanding the direction and magnitude of the magnetic field in this context.
Anurag98
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A uniform beam of positively charged particles is moving with a constant velocity parallel to another beam of negatively charged particles moving with the same velocity but in opposite direction separated by a distance d. Then, how should be the variation of magnetic field B along a perpendicular line drawn between the two beams?(For better view, imagine positive beam to be x-axis and negative beam to be y=1 line.)

I know that electric field will be there. But how the magnetic field will be generated and how will it vary?
 
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Hello Anurag, ##\qquad## :welcome: ##\qquad## !

Please post in homework and use the template -- it's mandatory

What do you know of the B-field generated by a current ##i## along the x-axis ?
 
BvU said:
Hello Anurag, ##\qquad## :welcome: ##\qquad## !

Please post in homework and use the template -- it's mandatory

What do you know of the B-field generated by a current ##i## along the x-axis ?
Thanks. I will take care of this from now on.
 
BvU said:
Hello Anurag, ##\qquad## :welcome: ##\qquad## !

Please post in homework and use the template -- it's mandatory

What do you know of the B-field generated by a current ##i## along the x-axis ?
It follows Biot-Savarts Law. That is ##{μ(i×dl)} /{r^2}##. (I am not able to produce it in fraction expression)
 
I moved it to homework, but you must still show your effort before our helpers are allowed to help.
 
anorlunda said:
I moved it to homework, but you must still show your effort before our helpers are allowed to help.
But I only know about current producing Magnetic field and not about charge beam producing magnetic field
 
BvU said:
Hello Anurag, ##\qquad## :welcome: ##\qquad## !

Please post in homework and use the template -- it's mandatory

What do you know of the B-field generated by a current ##i## along the x-axis ?
But it is charge beam and not a current carrying wire. Are both the above to be the same situations for magnetic field? If yes, then how?
 
See #5. Remember that current = moving charge
 
BvU said:
See #5. Remember that current = moving charge
So can we solve it using Ampere's circuital law?
As ##\vec{B}.{d\vec {l}} =μi=\frac{qv} {x}## But if it is so, then what should we take x?
 
  • #10
Anurag98 said:
But it is charge beam and not a current carrying wire
What's the difference :wink: ?

Let a to b be on the x-axis, one unit of distance apart (1m).
How much charge per unit time goes from a to b on the x-axis if there is a current ##i## ?
And how much charge per unit time goes from a to b on the x-axis if there is a beam of particles with charge q that move with velocity ##v##.

Conclusion ?

Note that your exercise asks for a qualitative answer.
 
  • #11
##
\vec{B}.{d\vec {l}} =μi \ ## I recognize. ##μ i=\frac{qv} {x} ## misses a ##\mu## .
What is the direction of ##\vec v## in your exercise ?
So what direction for ##x## ? for ##\vec B## ?
 
  • #12
BvU said:
What's the difference :wink: ?

Let a to b be on the x-axis, one unit of distance apart (1m).
How much charge per unit time goes from a to b on the x-axis if there is a current ##i## ?
And how much charge per unit time goes from a to b on the x-axis if there is a beam of particles with charge q that move with velocity ##v##.

Conclusion ?

Note that your exercise asks for a qualitative answer.
Okay. I understood. From what I am able think is that the field varies radially from each current and that we can use principle of superposition?
 
  • #13
You got it.
But be careful...:rolleyes:
 
  • #14
BvU said:
##
\vec{B}.{d\vec {l}} =μi ## I recognize. ##\μ i=\frac{qv} {x} ## misses a ##\mu## .
What is the direction of ##\vec v## in your exercise ?
So what direction for ##x## ? for ##\vec B## ?
My mistake for μ. Please see # 12.
 
  • #15
BvU said:
You got it.
Thanks for your help. :)
 
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