Calculating Magnetic Field of Two Wires at a Point (x, y)

In summary, the problem involves two wires carrying currents in the x- and y-directions, and the question asks for the magnitude of the magnetic field at a given point. The correct answer is obtained by finding the individual magnetic fields for each wire and adding them together, taking the absolute value of the sum. This is because the magnetic fields from each wire are in opposite directions at the given point.
  • #1
twalters84
14
0

Homework Statement



One wire, lying on the x-axis, carries a current of 8.0 A in the positive x-direction. Another wire, lying on the y-axis, carries a current of 12 A in the positive y-direction. What is the magnitude of the magnetic field at (x, y) = (8.0 cm, 12.0 cm)?

Homework Equations



B = (uI) / (2*PI*r)

u = 4*PI*10^-7

The Attempt at a Solution



First, I found each magnetic field seperately.

B1 = ((4*PI*10^-7)(12)) / (2*PI*(8/100)) = 3*10^-5 T
B2 = ((4*PI*10^-7)(8)) / (2*PI*(12/100)) = 1.3*10^-5 T

This is the point I am stuck. The answer key says the answer is 1.7*10^-5 T. I see that you can get that answer by:

3*10^-5 T - 1.3*10^-5 T = 1.7*10^-5 T

However, I do not understand the reasoning behind this. Could somebody explain this to me? Thanks in advance.


Travis Walters
 
Physics news on Phys.org
  • #2
For the Ix, the field at the given pt is toward +ve z, and for Iy, the field is toward -ve z.

Think about how the magnetic field lines are circular about the wire. Here, at the given point, they are in opp directions.
 
  • #3
Hey there,

I see what you mean about them being in opposite directions.

However, since B1 is in the negative Z direction, would that answer be -3*10^-5 T instead of 3*10^-5 T? Likewise, since B2 is in the positive Z direction, would that answer be 1.3*10^-5 T instead of -1.3*10^-5 T?

If that is the case adding these two quantities togather would yield -1.7*10^-5 T and not 1.7*10^-5 T correct? Is the magnitude the absolute value or should it be negative?

Thanks once again for any clarification.


Travis Walters
 
  • #4
The magnitude is simply the absolute value without regard to the sign and so is always +ve.
 

1. What is a magnetic field?

A magnetic field is a region in space where magnetic forces can be detected. It is produced by moving electric charges and can be described by its direction and strength.

2. How is a magnetic field measured?

A magnetic field is measured using a device called a magnetometer. This device detects the strength and direction of the magnetic field and can provide quantitative measurements.

3. What are the uses of magnetic fields?

Magnetic fields have a wide range of uses in various industries. They are used in compasses for navigation, electric motors for converting electrical energy into mechanical energy, and in medical imaging techniques like MRI machines.

4. How does a magnetic field affect objects?

A magnetic field can exert a force on certain objects, depending on their magnetic properties. Ferromagnetic materials (such as iron, nickel, and cobalt) are strongly affected by magnetic fields, while non-magnetic materials (such as wood and plastic) are not affected.

5. Can magnetic fields be harmful to humans?

In general, the magnetic fields found in our daily lives are considered safe and have no harmful effects on humans. However, extremely strong magnetic fields, such as those found in MRI machines, can potentially cause health risks and should be used with caution.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
276
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
783
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
339
  • Introductory Physics Homework Help
Replies
1
Views
592
  • Introductory Physics Homework Help
Replies
9
Views
916
  • Introductory Physics Homework Help
Replies
2
Views
982
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top