How Many Turns of Wire Does the Coil Have?

[feedmeister]

Homework Statement

A bar magnet with magnetic dipole moment 0.51 A m^2 lies on the negative x-axis, as shown in the diagram. A compass is located at the origin. Magnetic North is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 1.5 cm, connected to batteries not shown in the picture. The distance from the center of the coil to the center of the compass is 9.2 cm. The distance from the center of the bar magnet to the center of the compass is 22.5 cm. A steady current of 0.632 amperes runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass.

How many turns of wire are in the coil?

Homework Equations

$$B_{loop} = \mu_{0}2\pi R^{2}I/{4\pi}(z^{2}+R^{2})^{3/2}$$
$$B_{magnet} = \mu_{0}2\mu/4\pi r^{3}$$
$$B_{earth}$$= 2 E-5 Tesla

$$\mu_{0}/4\pi = 10^{-7}$$
I = 0.632 A
$$\mu = 0.51 A m^{2}$$

The Attempt at a Solution

I have been trying to do # of turns = $$(B_{earth} - B_{magnet}) / B_{coil}$$
and got 100.1271 but it's not the right answer. Can anyone help with what I'm doing wrong?

Attached is a diagram of the problem.

Thanks and regards,

 

[feedmeister]

Yeah I figured it out. It's actually just Bmagnet/Bcoil.

Thanks,

 

[Moetasim]

Hello ,

Thank you for sharing your attempt at solving this problem. It seems like you have a good understanding of the equations and concepts involved in finding the number of turns in a coil. However, there are a few things that may have led to an incorrect answer.

Firstly, I would recommend double-checking your units. In the equation for B_{loop}, the units for R and z should be in meters, while the units for I should be in amperes. Additionally, the units for B_{magnet} and B_{earth} should be in tesla, not amperes per meter. Making sure all units are consistent and in the correct form can help avoid errors in calculations.

Secondly, it may be helpful to break down the problem into smaller steps. For example, you could first calculate the magnetic field from the loop of wire at the location of the compass, using the given dimensions and current. Then, you could calculate the magnetic field from the bar magnet at the same location. Finally, you can subtract these two values to find the total magnetic field at the location of the compass. This total magnetic field can then be used in your equation to find the number of turns in the coil.

I hope this helps guide you towards the correct solution. Keep up the good work!

Best,