Net Magnetic Field of current carrying wires:

[spriter]

Homework Statement

http://img33.imageshack.us/img33/4547/walker4ech22pr054.jpg

Two long, straight wires are oriented perpendicular to the page, as shown in the figure . The current in one wire is I-1 = 3.0 A, pointing into the page, and the current in the other wire is I-2 = 4.0 A, pointing out of the page.

Question: Find the magnitude and direction of the net magnetic field at point P.

Homework Equations

Equations: B = u0*I/2*pi*r - where u0 = 4*pi * 10^-7 ( T * m/A), I = current, and r = distance from wire

The Attempt at a Solution

I found the magnetic field of both the wires at point P by using the above equation and the distance for I-1 as .05 meters and distance (r) for I-2 by using Pythagorean theorem .05^2 + .05^2 = c^2, etc - came out to about .071 meters.

After finding the two magnetic fields, I see that the magnetic fields are pointing in the opposite direction at point P, so I subtract them, but that is the wrong answer for the net magnetic field.

 

[BigJDubs]

Am I not subtracting the magnetic fields correctly, or is there something else I am missing? You have applied Ampere's law correctly, but the magnetic fields are not "pointing in opposite direction" at point P, they are pointing in perpendicular directions. Since the two currents are perpendicular to each other (as shown in the figure), the net magnetic field will be the vector sum of the two individual fields, instead of subtracting them. Hence, the net magnetic field at point P will be: B = √(B1^2 + B2^2)where B1 and B2 are the individual fields due to I-1 and I-2 respectively. The direction of the net magnetic field can be found using the right hand rule. Hope it helps.

 

[tomcue]

Thank you for providing your solution to this problem. Your approach is correct, but there are a few things that need to be addressed.

Firstly, the equation you have used to calculate the magnetic field is only applicable for a single long, straight wire. In this case, we have two wires, so we need to use a different equation to calculate the net magnetic field. The correct equation for this situation is given by the superposition principle:

Bnet = B1 + B2

Where B1 and B2 are the individual magnetic fields of the two wires.

Secondly, when using this equation, it is important to consider the direction of the magnetic fields. In this case, the magnetic field of the first wire (I-1) is pointing into the page, while the magnetic field of the second wire (I-2) is pointing out of the page. This means that the two fields are in opposite directions, so when you add them together, you will get a net magnetic field of 0 at point P.

I hope this helps clarify your solution. Keep up the good work!