Problem with find angle btw vectors (magnetism problem)

In summary, the magnetic force acting on a 25 cm wire carrying a current of 4.5 A along the z axis, with the components Bx = 0.10 T and By = 0.13 T, can be calculated using the equation F=ILB(sin theta), where theta is the angle between the current and the magnetic field. Since Bx and By are in the x-y plane, the resultant magnetic field is in the x-y plane as well, making theta invariably 90 degrees. By using this information, the correct answer can be obtained.
  • #1
crevin
2
0
1. Homework Statement

The x, y, and z components of a magnetic field are Bx = 0.10 T, By = 0.13 T, and Bz = 0.17 T. A 25 cm wire is oriented along the z axis and carries a current of 4.5 A. What is the magnitude of the magnetic force that acts on this wire?

2. Homework Equations
F=ILB (sin theta)
a^2 + b^2 = c^2


3. The Attempt at a Solution

Well, I have
F= (4.5A)(0.25 m)(B?) (sin theta)

Ok, so I know what I and L are--> 4.5 A and 0.25 m. I also know that B is going to be the vector sum of components x and y-->
0.10^2 + 0.13^2 = B^2, which gives me B= 0.16. I did not include z because the current is in the z direction (parallel direction = 0, since sin 0 = 0).

My question is: How do I find theta? Theta is the angle between the current and the magnetic field. I know the magnetic field = 0.16 and the direction of the current is in the z-axis, which is 0.17. I was thinking of doing the tan inverse of 0.16/0.17, but I don't think that answer is right.

Any ideas on how to find theta?

Thanks a lot for any help
 
Physics news on Phys.org
  • #2
theta is invariably 90 deg.
Theta is the angle between B & l. since u have taken Bx & By their resultant is in x-y plane & l is on z axis.
I hope i am clear.
 
  • #3
Yes! Thank Sourabh N for the help-- I've spent over an hour looking at it and couldn't get it!

I finally got the right answer with your advice.

Thanks A LOT!
 

1. What is the problem with finding the angle between vectors in a magnetism problem?

The main issue with finding the angle between vectors in a magnetism problem is that it requires a good understanding of vector math and trigonometry. It can also be challenging to visualize the vectors and their direction in a three-dimensional space.

2. How do you calculate the angle between two vectors in a magnetism problem?

To calculate the angle between two vectors in a magnetism problem, you can use the dot product formula: cosθ = (a · b) / (|a| * |b|), where a and b are the two vectors and θ is the angle between them. You can also use the cross product formula: sinθ = |a x b| / (|a| * |b|).

3. What are some common mistakes when finding the angle between vectors in a magnetism problem?

One of the most common mistakes is forgetting to convert the angle from radians to degrees or vice versa. Another mistake is not considering the direction of the vectors, which can result in an incorrect angle. It's also important to use the correct formula based on the given vectors (dot product or cross product).

4. How does the angle between vectors affect the strength of the magnetic force?

The angle between vectors in a magnetism problem is directly related to the strength of the magnetic force. The force will be strongest when the vectors are parallel to each other (θ = 0°) and weakest when they are perpendicular (θ = 90°). If the vectors are pointing in opposite directions (θ = 180°), the force will be zero.

5. What are some real-world applications of finding the angle between vectors in magnetism problems?

One example is in the design and construction of motors and generators, where the angle between magnetic fields is crucial for their proper functioning. Another application is in the field of navigation, where the angle between the Earth's magnetic field and a compass needle is used to determine direction. Magnetic resonance imaging (MRI) also utilizes the concept of finding the angle between vectors to create detailed images of the human body.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
101
  • Introductory Physics Homework Help
Replies
1
Views
199
  • Introductory Physics Homework Help
Replies
4
Views
252
  • Introductory Physics Homework Help
Replies
3
Views
925
  • Introductory Physics Homework Help
Replies
2
Views
520
  • Introductory Physics Homework Help
Replies
2
Views
195
  • Introductory Physics Homework Help
2
Replies
37
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
885
  • Introductory Physics Homework Help
Replies
17
Views
278
  • Introductory Physics Homework Help
Replies
5
Views
192
Back
Top