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

[aChordate]

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.

 

[rude man]

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'?

 

[aChordate]

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?

 

[rude man]

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?

 

[TSny]

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.

 

[rude man]

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 ...

 

[aChordate]

So, If I use ampere's law:

ΔB_||*Δl=μ₀I

What do I use for Δl? 7.0mm?

 

[rude man]

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.

 

[aChordate]

That's the equation I have in my textbook.

 

[rude man]

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.

 

[aChordate]

I don't have radius in the equation, I'm confused.

 

[rude man]

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.