Magnitude of magnetic fields of two perpendicular wires

[808techgeek]

Homework Statement

A) Find the magnitude of the net magnetic field at point P and point Q
B) Reverse the directon of the current for the wire on the x-axis

Homework Equations

B = μ0I/2πr

The Attempt at a Solution

Solution attempt attached. Only attempted part A, since I probably won't get part B correct if I'm not getting part A. Tried a few other permutations, but still arrived at similarly incorrect solutions. I'm a bit lost still. I thought adding the magnitudes of the B-fields at the points would give me the solution. Either that or my calculations are wrong, my algebra skills are out of practice.

 

[collinsmark]

Hello 808techgeek,

Welcome to Physics Forums!

Are both wires infinitely long? (It makes a difference)

If so, it looks like you are on the right track, but you need to be more careful with your sign conventions and the right-hand rule.

According to your work, out of the paper is defined as positive and into the paper is defined as negative. That's as good a convention as any. But once you have a convention, you need to stick to it.

Now you can break up the magnetic field at each point P and Q into their respective contributions of each wire. Let's start with point P.

B_P = B_P1 + B_P2.

And assuming that the wires are infinite in length and point P is on the same plane as the wires, all magnetic field components have directions perpendicular to the page, so we can give up our vector notation and deal with scalars:

B_P = B_P1 + B_P2

You already [essentially] have that on your attempted solution. But what you may have missed is that it doesn't mean that B_P1 and B_P2 are necessarily positive. One or both might be negative.

Use the right hand rule separately on B_P1 and B_P2 to figure out if each one is positive or negative.

Moving to point Q, you have on your attempted solution,

B_Q = B_Q1 - B_Q2

But that's not right. You should have

B_Q = B_Q1 + B_Q2

and then realizing that B_Q1 and/or B_Q2 can be positive or negative. In any case, whether they are both positive, one is negative, or both are negative, everything still gets added together.

(For example, if B_Q1 points out of the page it's positive. Otherwise if it points into the page it's negative. You can do this with one wire, and one point at a time.)

[Disclaimer: the only reason we get to give up vector notation here is because the magnetic fields caused by all wires are parallel to each other. If the wires were not infinite in length, or if points P and Q were not on the same plane as the wires, we couldn't do this and we'd have to treat everything as strictly vectors. That's because the magnetic fields wouldn't necessarily be pointing directly into or out of the page -- they'd be pointing somewhat into or out of the page at some angle. We could still solve the problem, but we'd have to deal with more vector components.]

 

[808techgeek]

Thank you so much for the help! I knew that I must have just misunderstood a simple concept.

 

[UnD3R0aTh]

i have a similar problem two perpendicular wires, y wire has current I from north to south, x wire has current 2I from west to east, at a point in top right corner of the square that has the wires as its diameters, and another point in the middle of the distance between y wire and right side of the square on the lower side of the square, which has flux of zero?

i figured it out, thx