Magnetic field. I on understanding this problem.

In summary, the student is having difficulty understanding how to solve the homework problem. They are stuck after trying to find the direction of the resultant vector. They are confused because there are many ways to specify the direction of a vector.
  • #1
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Homework Statement



Two long parallel conductors carry currents I_1 = 3.0A and I_2 = 3.0A, both directed into the page. Find the magnitude and direction of the resultant magnitude field at point p?


Homework Equations





The Attempt at a Solution



I need help with this problem. The professor only provided the answer but not the steps. I'm having a hard time understanding what to do. I can do all the other problems, but when it comes to a problem like this (with having to apply vectors) I do not know what to do. Help me.

First I tried drawing the magnetic fields (figure 2). Then I found the angles - 23 degrees and 67 degrees.

I am stuck after this. How do I solve using vectors?
 

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  • #3
what do you mean by tangential?
 
  • #4
The B field around a wire follows circles - at distance r, the B vector will be a tangent to the circle, centered on the wire, with radius r.

Is ##\vec{B}_1## the field due to ##I_1## and ##\vec{B}_2## the field due to ##I_2##?
If so, they are pointing in the wrong directions. Please see the accompanying link.
 
  • #5
oh yes, I am sorry. your correct. i miswrote the B1 and B2.
 
  • #6
OK - so... do you know how to add vectors?
 
  • #7
hmm is the special right triangle the triangle with the 90 degrees or is it the one with the added vectors?
 
  • #8
i know how to add vectors like moving head to tail, but not very well when it comes to the math.
 
  • #9
so at this point i would get a resultant vector that goes straight down. but I am confuse. do i do the x and y component for B1 and B2 separately or do i do the x and y component for the resultant component?
 
  • #10
To use x-y components you need to define an x and y-axis - which is not provided for you.
Instead you should use the head-to-tail triangle of vectors and your knowledge of trigonometry.

One special triangle you have is the pythagorean triplet 5-12-13 ... point P is at the right angle.
It is probable that the B vectors also make two sides of a special triangle. They do conveniently make a right-angle with each other. If the resultant vector does go straight down, then it must be 5-12-13 as well.

There are lots of ways of specifying the direction of a vector.
If you label the position of I1 as Q and I2 and R, then the straight down direction is the Q-R direction ... or "parallel to ##\overrightarrow{QR}##"
 

1. What is a magnetic field?

A magnetic field is a region in space where magnetic forces are present. These forces are created by moving electric charges or magnetic materials.

2. How is a magnetic field created?

A magnetic field is created by moving electric charges or magnetic materials. When electrons move through a conductor, they create a magnetic field. Similarly, magnetic materials have their own atomic alignment that creates a magnetic field.

3. What is the difference between a magnetic field and an electric field?

A magnetic field is created by moving electric charges, while an electric field is created by stationary electric charges. In addition, electric fields exert forces on electric charges, while magnetic fields exert forces on moving electric charges.

4. How is the strength of a magnetic field measured?

The strength of a magnetic field is measured in units of Tesla (T) or Gauss (G). One Tesla is equal to 10,000 Gauss. The strength of a magnetic field can also be measured using a magnetometer, a device that detects and measures magnetic fields.

5. What are some real-life applications of magnetic fields?

Magnetic fields have a wide range of practical applications, including compasses for navigation, electric motors, generators, MRI machines in healthcare, and magnetic levitation trains. They are also used in industries such as electronics, telecommunications, and energy production.

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