How Do You Calculate the Net Magnetic Field Between Two Wires?

[waywardtigerlily]

Ok, I have been working on this problem for about 2 hours now, and I still can't get the right answer..could someome help me?

two wires carry currents of I=5.12A in opposite directions and are separated by a distance of d0=9.33cm. (the wire on the left has I going up and the one on the right is going down) Calculate the net magnetic field at a point midway between the wires. Use the direction out of the page as the positive direction and into the page as the negative direction in your answer.

B. Calculate the net magnetic field at point p1- that is 9.32 cm to the right of the wire on the right.

C. calculate the net magnetic field at point p2- that is 19.3 cm to the left of the wire on the left.


To calculate B. I am using:

BR=uoI
2pi (p1/2)

BR= (4pi x 10^-7)(5.12)
(2Pi)(.0466)

= 2.19742 x 10^-5 T

BL=uoI
2pi(p1+do)

BL= (4pi x 10^-7)(5.12)
2Pi(.1865)


Bnet= BR-BL
= 1.65 x 10 ^-5 T

Can anyone see what I am doing wrong? I assume for C you would use the same procedure and for the main question you would just use Bnet= B1+B2
Thanks!

 

[vincentchan]

just want to net u no, your notasion is hard to folow, plis don't write it dat way next time...
$$B_{right} = \frac{\mu_0 I}{2 \pi p_1}$$
and
$$B_{left} = \frac{\mu_0 I}{2 \pi (p_1+d_0)}$$

$$B_{total} = B_{right} - B_{left}$$
since $B_{right}$ and $B_{left}$ have different direction

Can anyone see what I am doing wrong? I assume for C you would use the same procedure and for the main question you would just use Bnet= B1+B2
Thanks!

your $B_{right}$ have a factor of one half at the bottom for some reason... is that because that is the formula for part a ?
and yes, in general, the total B field is the sum of its component

 

[thepatientmental]

It looks like you are on the right track with your calculations. The only thing I would suggest is to make sure you are using the correct distance for p1 and p2. In your calculations, you have used 0.0466 m for p1, but it should be 0.0465 m since it is halfway between the wires. Similarly, for p2, you have used 0.1865 m, but it should be 0.193 m since it is 19.3 cm to the left of the wire on the left.

Other than that, your calculations and method seem correct. Just make sure to double check your distances and units and you should get the correct answer. Good luck!