physics question please help mememe?

Question

Two parallel conductors carry currents in opposite directions, as shown in Figure P19.56. One conductor carries a current of 10.0 A. Point A is the midpoint between the wires, and point C is 5.00 cm to the right of the 10.0 A current. I is adjusted so that the magnetic field at C is zero.

Figure P19.56
http://www.webassign.net/sf5/p19_52.gif

(a) Find the value of the current I.
A
(b) Find the value of the magnetic field at A.
T

Answer 1

Ok, in this problem, you just have to know the ampere's law, that says :

integrate(B.dl) = Uo*I

in the case of the conductor, the magnetic field will be :

B = Uo*I / 2*pi*r

where : r is the distance, Uo = 4*pi*10^-7

pi = 3.1416.

Well, and the other thing you must know, is that in the case of your problem, the direction of the magnetic field depends on the direction of the current.

For the first conductor :

the distance will be 10 + 5 = 15 cm, and we are looking for it's current

Magnetic field at C : Uo*I / 2*pi*(15/100)

For the second conductor :

The distance will be 5 cm

Magnetic field at C : Uo*10 / 2*pi*(5/100)

But these magnetic field have diferent directions, so the magnetic field at C, will be :

Uo*10 / 2*pi*(5/100) - Uo*I / 2*pi*(15/100) = 0

10 / (5/100) = I / (15/100)

I =30 Amperes

Now that we have the current in the first conductor, we can find the magnetic field at A.

magnetic field at A :

Uo*30 / 2*pi*(5/100) - Uo*10 / 2*pi*(5/100)

Uo = 4*pi*10^-7

4*pi*10^-7*(30 - 10 ) / 2*pi*(5/100) = 2*10^-7*20*100 / 5

Magnetic field at A = 8*10^-5 (Tesla)

Answer 2

For B) Don't subtract I (Current).. Instead you need to add them. and you will get an answer of 1.6e-4..