Forces on current carrying wires

[flyingpig]

Homework Statement

Two long parallel conductors separated by 10.0 cm carry currents in the same direction. The first wire carries a current I₁ = 5.00 A, and the second carries I₂ = 8.00 A.

http://img52.imageshack.us/img52/7425/asasssf.th.png

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(a) What is the magnitude of the magnetic field created by I₁ and at the location of I₂
(b) What is the force per unit length exerted by I on I₂?

The Attempt at a Solution

For (a) it is

$$\left |\vec{B_1} | \right= \frac{\mu_{0} I_{1}}{2\pi d}$$

Then it is just a matter of plugging in the numbers and it should come out as 10^-5T

But my question is, why is it that we use r = 10.00cm? Shouldn't it be d + x?

http://img805.imageshack.us/img805/6568/asasss.th.png

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Now for (b), I am just confused with Newton's third Law. I just don't understand I am wrong.

Look at picture

http://img854.imageshack.us/img854/6568/asasss.th.png

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By the right hand rule - cross product - the force F₁ should be to the right, that is the Force exerted by wire 1 (which I forgot to label as the one on the right) on wire 2.

If I were to do the Math I get

$$\left | \vec{F_{12}} \right | = I_{1} l \left| \vec{B_1} \right|$$

$$\left | \vec{F_{12}} \right | = I_{1} \frac{\mu_{0} I_{1}}{2\pi d}$$

$$\frac{\left | \vec{F_{12}} \right |}{l} = \frac{\mu_{0} I_{1}^2}{2\pi d}$$

Which is wrong, but it should be $$\frac{\left | \vec{F_{12}} \right |}{l} = \frac{\mu_{0} I_{1} I_{2}}{2\pi d}$$ by Newton's third law

 

[SammyS]

In what direction do you want to take x?

 

[flyingpig]

To the right as in the picture

 

[cupid.callin]

then how will d+x be the position of green wire wrt blue wire ??

 

[flyingpig]

Not sure what you mean, but I added a picture

http://img805.imageshack.us/i/asasss.png/

 

[cupid.callin]

if F₁₂ means force on wire 1 due to wire 2

then F₁₂ = i₁ l B₁ where B₁ is the field at i₁ (Not due to i₁)

So B₁ = μ_oi₂/2πd

 

[cupid.callin]

Not sure what you mean, but I added a picture

http://img805.imageshack.us/i/asasss.png/

I know you added a pic ...

What is the magnitude of the magnetic field created by I₁ and at the location of I₂

It asks for b at i₂ ... so you must use the distance of i₂ from i₁

how did you came up with d+x ?

 

[flyingpig]

if F₁₂ means force on wire 1 due to wire 2

then F₁₂ = i₁ l B₁ where B₁ is the field at i₁ (Not due to i₁)

So B₁ = μ_oi₂/2πd

Yes, but isn't that what I have in http://img854.imageshack.us/i/asasss.png/?

It feels right to me, but I know it is wrong.

I know you added a pic ...

What is the magnitude of the magnetic field created by I₁ and at the location of I₂

It asks for b at i₂ ... so you must use the distance of i₂ from i₁

how did you came up with d+x ?

Oh okay, that is answered

 

[SammyS]

Question (a):
" What is the magnitude of the magnetic field created by I₁ and at the location of I₂ ?"

The location of I₂ IS a distance d from I₁. No need for x.

Seems very clear to me.

 

[flyingpig]

No that one is answered, I made it complicated

 

[cupid.callin]

Yes, but isn't that what I have in http://img854.imageshack.us/i/asasss.png/?

It feels right to me, but I know it is wrong.



Oh okay, that is answered

in eqn F = iBl

B is the field at location of wire ... i is current in wire and l is length of wire

B at wire 1 is due to wire 2(and not wire 1 itself) so for expression of B you use i₂ as i2 produce the current

 

[SammyS]

What question are you trying to answer?

 

[flyingpig]

http://img854.imageshack.us/img854/6568/asasss.th.png

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This picture, it should be F₂₁, but I cannot convince myself that it is. By the cross product I get a force F₁ to the right, which is the force of 1 exerted onto 2