Magnetic Field & 2 wires with same current

[sami23]

Homework Statement

Two long, straight, parallel wires, 10.0 cm apart carry equal 3.78A currents in the same direction. Find the magnitude and direction of the magnetic field at point 15.4 cm above one wire.

Homework Equations

B= (\mu₀I)/(2\pir)
\mu₀ = 4\pi * 10^-7
Use the right hand rule to find the direction of magnetic field

The Attempt at a Solution

(4\pi*10^-7)*3.78 / (2\pi0.154) * cos(\theta)*2
I'm not sure on how to go about solving this problem

 

[Stonebridge]

That's the correct formula for finding the flux density B at a point a distance r from a long straight wire carrying a current I
A diagram helps a lot here.
The two wires are L and R and we are looking along them, the current flowing into the page/screen.
The point we are interested in is at P.
The distances are shown.
Can you calculate the distance LP which you need to find the field due to L?

The magnitude and direction of the field at P is found by adding the two vectors for the forces due to L and R. These are shown as B_L and B_R.
Do you know how to add vectors?


Remember, the magnetic field around a wire is a circle with the wire at the centre.
If the current is into the page the field is clockwise around the wire.

 

[sami23]

LP = \sqrt{0.154^2+0.1^2} = 0.1836 m

B = (4\pi*10^-7)(3.78) / (2\pi*0.1836) = 4.12 T

 

[Stonebridge]

You have calculated B_L
The answer should be 4.12μT not 4.12T
You also need to calculate B_R
(It's the same formula but with r=0.154m)

When you have both B_L and B_R you need to add the vectors. Do you know how to do that?

 

[sami23]

Yes, Thanks so much.