Infinite Parallel wires Magnetic field

[Funnynick]

Homework Statement

Two long parallel wires each carry a current of 5.0A directed to the east. The two wires are separated by 8c.m. What is the magnitude of the magnetic field at the point that is 5.0 cm from each of the wires.

Homework Equations

B= \frac{μI}{2∏R}

The Attempt at a Solution

I know the equations and how to work a simple problem. The question i need answered is how do i find the magnetic field 5 cm away from each wire when they are separated by 8 cm.? so i set one wire UI/2∏(.5) to get the first wire magnetic field, but i need to find the other wire at the same point so its going to be either UI/ 2∏(.13) or UI/2∏(.03). Or am i completely wrong any help would be awesome.oh and I am not sure if ∏ is the pi symbol but that is what i used it for.

Thanks

 

[Doc Al]

You want to find the points that are 5 cm from both wires. Hint: Draw two circles and see where they intersect.

(You can also use a lower case for π.)

 

[Funnynick]

So when i draw the two circles i am getting intersects of the 2 B-fields from each wire at 4 cm in between them at 2 points, is that correct?>

So i calculated for the 4cm radius and multiply my result B by 2? to get the magnetic field between the two wires at 5 cm from each wire? i am Confused sorry

 

[Doc Al]

So when i draw the two circles i am getting intersects of the 2 B-fields from each wire at 4 cm in between them at 2 points, is that correct?>

Yes.

So i calculated for the 4cm radius

No, the radius about each wire is 5 cm.

and multiply my result B by 2?

No, you have to add the fields like vectors.

Draw a diagram and show the direction of the vectors. Then you can add them properly.

 

[Funnynick]

if i just do \frac{μ(5)}{2∏(.04)} it gives me 25Micro tesla and the answer is 24 micro tesla so what am i missing i have to subtract something tiny

 

[Doc Al]

if i just do \frac{μ(5)}{2∏(.04)} it gives me 25Micro tesla and the answer is 24 micro tesla so what am i missing i have to subtract something tiny

For one thing, you are using r = 0.04 instead of 0.05 like you should be using.

 

[StrawHatGary]

what is μ in this equation then? If the answer is 24 i solved for μ and got 15.2793 and that doesn't sound right, how do you come up with the charge?

 

[Doc Al]

what is μ in this equation then? If the answer is 24 i solved for μ and got 15.2793 and that doesn't sound right, how do you come up with the charge?

μ is the permeability of free space. It's a constant, not something you solve for. See: Magnetic Field of Current

 

[zbryant3]

Old question, but why don't the two wire's magnetic fields cancel each other out? The way I pictured it they cancel each other out by symmetry. When calculating the components of each magnetic field vector produced by each wire, if I make the angle negative in one case and positive in the other, I get the correct answer. Why does the angle become negative? Picture is of my drawing, I made the upper angle positive and the lower angle negative.
EDIT1: Don't know why the picture isn't showing up but its just of the problem.
EDIT2: Ok nevermind I figured out why one of the angles is positive and the other is negative.

https://mail.google.com/mail/u/0/?ui=2&ik=7f5efe1f9c&view=fimg&th=158eb73c61b1ab14&attid=0.1&disp=inline&safe=1&attbid=ANGjdJ81T8_js0QWyNdksPFwEkfX1N3_4iu1y6LAfTJnCP786Q1b0VCRtbhDva7iKX7xvBgiYEq24E6B4ytZWroQfj1MxIGQzo_Wp-ZKvwGypuiaiJsL-bjbbXYwUEE&ats=1481419116210&rm=158eb73c61b1ab14&zw&sz=w1920-h1012