Magnetic field from two wires and magnitude

[tarellan]

Homework Statement

can someone please help? I am having major problems with physics right now :(

Each of the wires carries a current of magnitude I. The current in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance between the wires is 2d. The x-axis is perpendicular to the line connecting the wires and is equidistant from the wires.


a.) Point M is located a distance 2d from the midpoint between the two wires. Find the magnitude of the magnetic field B_1M created at point M by wire 1.
*Express your answer in terms of I, d, and appropriate constants.

b.)Find the magnitude of the net magnetic field B_M created at point M by both wires.
*Express your answer in terms of I, d, and appropriate constants.

Homework Equations

The Attempt at a Solution

I got the B1L created by wire 1 by point 1 only.
so I thought since they have the same current and distance, they will have the same magnitude, so I just add them. But I got it wrong.
one of the hint says "find the direction of B"
I am confused how to find the direction for wire 1 and 2 at point M.

 

[diazona]

Well, let's take it one step at a time. First, pretend wire 2 doesn't exist, and find the magnetic field (magnitude and direction) produced by wire 1 at point M. Do you know how to start doing that? (Hint: use the right-hand rule for the direction)

 

[nlightner]

Hi there!

I'm sorry to hear that you're having trouble with physics. It can be a challenging subject, but with some practice and understanding of the concepts, I'm sure you'll be able to tackle this problem and many others.

Let's start by reviewing the concept of magnetic fields. A magnetic field is a vector quantity, meaning it has both magnitude and direction. It is represented by the symbol B and is measured in units of Tesla (T). The direction of the magnetic field is given by the right-hand rule, where you curl your fingers in the direction of the current and your thumb points in the direction of the magnetic field.

Now, let's apply this to the problem at hand. We have two wires, each carrying a current of magnitude I. The magnetic field created by a wire at a point M is given by the formula B = μ0I/2πr, where μ0 is the permeability of free space (a constant) and r is the distance from the wire to the point M. Since we are dealing with two wires, we will need to calculate the magnetic field created by each wire separately and then find the net magnetic field by adding them together.

For part a), we are asked to find the magnitude of the magnetic field created by wire 1 at point M. Since point M is located a distance 2d from the midpoint between the two wires, the distance from wire 1 to point M is d. Using the formula mentioned earlier, we can write the magnetic field created by wire 1 at point M as B_1M = μ0I/2πd. Note that this is the magnitude of the magnetic field, so we don't need to worry about the direction at this point.

For part b), we need to find the magnitude of the net magnetic field created by both wires at point M. To do this, we first need to find the magnetic field created by wire 2 at point M. Using the same formula, we can write the magnetic field created by wire 2 at point M as B_2M = μ0I/2πd. Now, to find the net magnetic field, we need to add these two fields together, taking into account their directions. Since wire 1 is directed out of the page and wire 2 is directed into the page, their magnetic fields will have opposite directions. This means we need to subtract the two fields, giving us a net magnetic