M & G's Problem(2parallel conductors) (1 Viewer)

[Shire-miss]

This question is about two parallel current-carrying conductors and comes from the physics in context textbook so if anyone could explain it to me that would be great!

"Two straight parallel conducting wires carry currents of 1A and 2A respectively in opposite directions and cross a metre rule at the 50cm and 80 cm marks (ie, they lie 30cm apart) At which point on the rule is the net magnetic field zero???????'

the answer is at the 20 cm mark...so how do we go about getting this answer cos i'm confused...

 

[Dangar]

K well you can see that the current is going in opposite directions so you can figure out the directions of the magnetic fields, and thus see that they will cancel out to create a net magnetic field of zero somewhere to the left of wire 1 which is carrying 1A.

Then you have to mathematically balance the two magnetic fields:

B= (2x10^-7 x I) / (2 x pi x r)

where pi is 3.14 (I don't know how to get that symbol)
and r1 is the distance between the point and wire 1
and r2 is the distance between the point and wire 2

so:

(2 x 10^-7 x 1) / (2 x pi x r1) = (2 x 10^-7 x 2) / (2 x pi x r2)

the (2 x pi) and 2 x 10^-7 cancel out leaving us:

2 x r1 = r2

but r2= r1 + 30 (look at your diagram)

so we solve simultaneously and get r1 equal to 30

then seeing as wire one is positioned at 50cm, move to the left 30cm and therefore at the 20cm mark the net magnetic field will be zero.


I hope you can follow this, I know it looks confusing on the screen but if you write it out it should all make sense!

 

[wogboy]

Use the formula:
B = k * I / d, where:

B = magnetic field strength (T)
k = constant = 2*10^(-7)
I = current (A)
d = distance from wire (m)

so let:
B1 = magnetic field due to 1A wire (A)
B2 = magnetic field due to 2A wire (A)
x = position on the ruler (m)

therefore:

B1 = k * 1 / (x - 0.5)
B2 = k * (-2) / (x - 0.8)

(don't forget to convert the centremetres to metres when doing these calculations. Also you'll notice in the formula for B2 that the current is negative -2A since it travels in the opposite direction to the current in the 1A wire).

The net magnetic field, Bn is simply the sum of B1 and B2

Bn = k/(x - 0.5) - 2*k/(x - 0.8)

so now we have to solve this equation for Bn = 0 (where the net magnetic field is zero).

0 = 1/(x - 0.5) - 2/(x - 0.8)
1/(x-0.5) = 2/(x-0.8)
2 * (x - 0.5) = x - 0.8
2x - 1 = x - 0.8
x = 1 - 0.8
x = 0.2 m

so the zero magnetic field occurs at the point on the ruler which is 20 cm.

[Edit] Beaten to it by dangar.

 

[Shire-miss]

thanx for that guys... your replies explained a lot my teacher didn't