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

  • #1
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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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  • #2
BvU
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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 ?
 
  • #3
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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 ?
Thanks. I will take care of this from now on.
 
  • #4
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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 ?
It follows Biot-Savarts Law. That is ##{μ(i×dl)} /{r^2}##. (I am not able to produce it in fraction expression)
 
  • #5
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I moved it to homework, but you must still show your effort before our helpers are allowed to help.
 
  • #6
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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
 
  • #7
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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 ?
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?
 
  • #8
BvU
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See #5. Remember that current = moving charge
 
  • #9
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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
BvU
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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
BvU
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##
\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
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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
BvU
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You got it.
But be careful...:rolleyes:
 
  • #14
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##
\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
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You got it.
Thanks for your help. :)
 
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