# Solve Magnetic Field from Perpendicular Wires Carrying Same Current

• NotaPhysicsMan
In summary, the conversation discusses finding the net magnetic field at point P created by two wires with perpendicular currents. The magnitude and direction of the field are determined using the equation B=uI/2pieR and the right hand rules, resulting in a value of 1.96x10^-4 T downwards. There is a correction made regarding the angle used in the calculation and the final answer is confirmed to be 60 degrees.
NotaPhysicsMan
Ok, since I got little feedback, I will try it again, but please help. It's due tomorrow!

The drawing (attachment) shows two wires that carry the same current of I=85.0 A are are oriented perpendicular to the plane of the paper. The current in one wire is directed out of the paper, while the current in the other is directed into the paper. Find the magnitude and direction of thenet magnetic field at point P.

For those who can't get the attacment, the drawing is simple:

Code:
    P

X       0
A equilateral triangle with sides of 0.150 m, X being current into and 0 being out of.

Ok it seems that I just have to use: B=uI/2pieR to get the magnitude of the diagonal.

Using the right hand rules I draw two circlular fields reaching point P sort of like venn diagrams. Ok the radius is really just the distance from the currents to the P, so R=0.150m.

B=4pie x 10^-7 (85.0A)/ 2pie (0.150m)
B=1.133x10^-4 T.

Next:

I have two right angle triangles split in half, with the x-directions cancelling each other and the y-direction adding together going downwards. Ok so each of the angles will give 60/2=30. So 1.133x10^-4 T(cos30)=9.812x10^-5T for the y and for x=5.665x10^-5 T. X's will cancel. And for Y's or the net magnetic field is:

(2 x 9.812x10^-5T)=1.96x10^-4 T downwards?

Ok 1 other thing my friend did was just use cos 60 instead of cos 30. The answer comes out to be 1.133x10^-4, which is in fact correct according to my teacher. BUT why would you use 60 degrees. It's an equilateral triangle but you can't just you the right triangle relationships unless you split the triangle up into halves, in which case you would have 30 degrees each...

#### Attachments

• TriangleCurrent.GIF
1.2 KB · Views: 534
NotaPhysicsMan said:
A equilateral triangle with sides of 0.150 m, X being current into and 0 being out of.

Ok it seems that I just have to use: B=uI/2pieR to get the magnitude of the diagonal.
You are substituting values too early and obcsuring the physics. Work it out algebraically and plug in the values at the end.

$$\vec B = \frac{\mu_0I}{2\pi R} \hat I \times \hat r$$

So at P the field B from the left wire is 90 deg to the radius so it makes a 60 deg angle to the vertical. Its vertical component is Bcos(60). The same for the wire from the right. The horizontal components are Bsin(60) (right) and Bsin(60)(left) so they cancel.

$$B_P = 2Bcos(60) = 2\frac{\mu_0I}{2\pi R}(.5) = \frac{\mu_0I}{2\pi R}$$

AM

Darn, I screwed up the degrees...ok 60 is right. Thanks.

## What is a magnetic field?

A magnetic field is a region in which a magnetic force can be observed. It is produced by moving electric charges and can be visualized as lines of force that surround a magnet or electric current.

## How do perpendicular wires carrying the same current create a magnetic field?

Perpendicular wires carrying the same current create a magnetic field because the current flowing through the wires produces a magnetic force perpendicular to the direction of the current. The interaction between the magnetic fields of the wires produces a combined magnetic field that is perpendicular to both wires.

## What is the direction of the magnetic field produced by perpendicular wires carrying the same current?

The direction of the magnetic field produced by perpendicular wires carrying the same current can be determined by using the right-hand rule. The magnetic field will be perpendicular to both wires and will point in the direction determined by the right-hand rule.

## How can the strength of the magnetic field be calculated?

The strength of the magnetic field produced by perpendicular wires carrying the same current can be calculated using the equation B = (μ0 * I) / (2π * r), where B is the magnetic field strength, μ0 is the permeability constant, I is the current, and r is the distance between the wires.

## What is the significance of the magnetic field produced by perpendicular wires carrying the same current?

The magnetic field produced by perpendicular wires carrying the same current has important applications in electromagnetism, such as in motors, generators, and transformers. It also plays a crucial role in the behavior of charged particles in magnetic fields, which is important in fields such as particle physics and astrophysics.

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