Force on a Moving Charge Due to a Current-Carrying Wire

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Homework Help Overview

The discussion revolves around the force experienced by a moving charge near a current-carrying wire. The charge is specified as q+ 4.5 x 10^-9 C, positioned 7.0 mm from the wire, and moving away from it with a velocity of 3.0 x 10^4 m/s. The wire carries a current of 2.2 A. Participants are exploring the relationship between the charge's motion, the current, and the resulting magnetic field.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the right-hand rule to determine the direction of the force on the charge. There are questions about the magnetic field's calculation and the relevance of Ampere's law. Some participants express uncertainty regarding the parameters needed for calculations, such as the distance from the wire.

Discussion Status

The discussion is ongoing, with participants actively questioning assumptions about the direction of the force and the application of Ampere's law. There is a mix of agreement and disagreement regarding the interpretations of the magnetic field and the force's direction, indicating a productive exploration of the topic.

Contextual Notes

Some participants note confusion regarding the application of Ampere's law and the integration around a closed path versus a radius. There is a lack of consensus on the correct interpretation of the magnetic field's direction and the parameters involved in the calculations.

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Homework Statement


A charge q+ 4.5 x 10^-9 is located a distance of 7.0 mm to the right of a wire and is moving directly away from the wire with a velocity of v =3.0 x 10^4 m/s, as shown in the drawing (drawing shows charge moving to the right and current moving upwards). The wire carries a current I= 2.2 A. What is the force (magnitude and direction) felt by the charge due to the wire?


Homework Equations



B=F/ (|q|vsinθ)

The Attempt at a Solution



According to the right hand rule, the Force would be pointing downward.
 
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aChordate said:

Homework Statement


A charge q+ 4.5 x 10^-9 is located a distance of 7.0 mm to the right of a wire and is moving directly away from the wire with a velocity of v =3.0 x 10^4 m/s, as shown in the drawing (drawing shows charge moving to the right and current moving upwards). The wire carries a current I= 2.2 A. What is the force (magnitude and direction) felt by the charge due to the wire?


Homework Equations



B=F/ (|q|vsinθ)

The Attempt at a Solution



According to the right hand rule, the Force would be pointing downward.

That is correct.

So how about using your 'relevant equation'?
 
B=F/ (|q|vsinθ)

B= F / (4.5x10^-9)*(3.0x10^4)*(sin 90)

I am not sure how to find the magnetic field. I would use the current I = 2.2 A? And is sin90 correct?
 
aChordate said:
B=F/ (|q|vsinθ)

B= F / (4.5x10^-9)*(3.0x10^4)*(sin 90)

I am not sure how to find the magnetic field. I would use the current I = 2.2 A? And is sin90 correct?

Sin(90) is correct.
How about using Ampere's law?
 
aChordate said:
A charge q+ 4.5 x 10^-9 is located a distance of 7.0 mm to the right of a wire and is moving directly away from the wire with a velocity of v =3.0 x 10^4 m/s, as shown in the drawing (drawing shows charge moving to the right and current moving upwards). According to the right hand rule, the Force would be pointing downward.

Are you saying that the force would be in the opposite direction of the current in the wire? I don't think that's correct.
 
TSny said:
Are you saying that the force would be in the opposite direction of the current in the wire? I don't think that's correct.

The charge is moving in the +x direction and the current is flowing in the +y direction, so at x > 0 the B field is in the -z direction:

v x B =+i x (-k) = +j rats! TSny is right, it flows same direction as the current. OP take note ...
 
So, If I use ampere's law:

ΔB||*Δl=μ0I

What do I use for Δl? 7.0mm?
 
aChordate said:
So, If I use ampere's law:

ΔB||*Δl=μ0I

What do I use for Δl? 7.0mm?

You should look up ampere's law. No, it's not 7mm.
 
That's the equation I have in my textbook.
 
  • #10
aChordate said:
That's the equation I have in my textbook.

I don't think so.
Ampere's law integrates around a closed path, not along a radius.
 
  • #11
I don't have radius in the equation, I'm confused.
 
  • #12
aChordate said:
I don't have radius in the equation, I'm confused.

Yes you do. 7mm is the radius of a circle surrounding the wire. You're supposed to integrate around the circle.

BTW that's the problem with your other post so I will not answer that one again until you're clear on this point.
 

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