Finding Total B-Field and Direction in a Wire-Magnet System

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Homework Help Overview

The discussion revolves around calculating the total magnetic field at a specific point in a system involving a long, straight wire carrying a current and a uniform magnetic field. The wire is oriented along the y-axis with a current flowing in the -y-direction, while the uniform magnetic field is directed in the +x-direction. Participants are tasked with determining both the magnitude and direction of the total magnetic field at the point located at x = 0, z = 1.00 m.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the calculation of the magnetic field due to the wire using the equation B = (mu_0 * I) / (2 * pi * r) and express uncertainty about how to proceed with finding the direction of the magnetic field.
  • Some participants question the missing information regarding the magnitude of the uniform magnetic field in the x-direction and suggest that it is essential for the calculation.
  • There is a focus on understanding how to add the two magnetic field vectors and the implications of vector addition in this context.
  • One participant expresses confusion about finding the angle related to the total magnetic field and seeks further clarification.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance on vector addition and the need to consider both magnitude and direction for the total magnetic field. There is recognition of the importance of correctly identifying the direction of the magnetic field from the wire and how it interacts with the uniform magnetic field. However, there is no explicit consensus on the final approach or solution yet.

Contextual Notes

Participants note the absence of the magnitude of the uniform magnetic field, which is critical for completing the calculations. There is also an emphasis on the need to consider the components of the magnetic fields as vectors rather than scalars, which affects how they are summed.

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Homework Statement



A long, straight wire lies along the y-axis and carries a current I = 8.00 A in the -y-direction . In addition to the magnetic field due to the current in the wire, a uniform magnetic field with magnitude is in the +x-direction.

What is the magnitude of the total field at the point x = 0, z = 1.00 m in the xz-plane?

What is its direction? from x to z axis.

Homework Equations



Using magnetic field equation B = (mu_0 *I)/2*pi*r

The Attempt at a Solution



B = (mu_o*I)/2*pi*r = (4pi x 10^-7)(8.00A)/2pi*(1.00m) = 1.6 x 10^-6 T

using the same equation B = (mu_o*I)sin(theta)/2*pi*r, but I am not sure how to continue this problem.

Can someone help me how to calculate for the direction for this B-field that goes from x to z axis?

Thanks
 

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I can't see the attachment yet, but I'll try to offer as much advice as I can without it.

You have found the magnitude of the B field from the wire correctly. You also didn't give the magnitude of the constant field in the x direction. I assume you forgot to put it in, since its seems to be something that needs to be given. Here are some hints to help you get to the answer.

Hints:

What direction does the B field from the wire point in?

If you know this then you know the two B vectors, both magnitude and direction. Now the total B field will be their sum, correct? How do you add these two vectors?
 
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G01 said:
I can't see the attachment yet, but I'll try to offer as much advice as I can without it.

You have found the magnitude of the B field from the wire correctly. You also didn't give the magnitude of the constant field in the x direction. I assume you forgot to put it in, since its seems to be something that needs to be given. Here are some hints to help you get to the answer.

Hints:

What direction does the B field from the wire point in?

If you know this then you know the two B vectors, both magnitude and direction. Now the total B field will be their sum, correct? How do you add these two vectors?

Thank for the advice.

From the RHR, the magnetic field is pointing in the x-axis direction, similar to B_o.

The value for B_o is given as 1.50 x 10^-6 T, so the total B field will then be 1.50 x 10^-6 + 1.6 x 10^-6 T = 1.0 x 10^-7 T.

I am still confuse on how to find the angle, can you further explain?

Thanks
 
whitetiger said:
The value for B_o is given as 1.50 x 10^-6 T, so the total B field will then be 1.50 x 10^-6 + 1.6 x 10^-6 T = 1.0 x 10^-7 T.

This is not the correct sum of the vectors. Remember Vectors don't add like real numbers. Here you have a horizontal component, and a vertical component. The sum vector will be the hypotenuse of the triangle they form. Does this help you remember how to find the sum? Then, use trig to find the angle. Does this help?
 

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