Calculating Radial Distance in a Toroidal Coil: Step-by-Step Guide

[emilyelizabeth]

Radial Distance

In class, I measured the field strength of a toroidal coil at various distances.
I used a linear track to move the hall probe along the azimuthal field at certain positions.
How do i convert the distance into radial distance if the inner conductor is at radius 2.5 cm?

 

[emilyelizabeth]

:(

d;

 

[UltrafastPED]

Using the measured coordinates you could plot the points where the measurements were taken, and then measure each from the center of the toroid.

 

[emilyelizabeth]

Yeah but all we used was distance ? the only helpful thing we really know is the radius of the inner toroid.

 

[emilyelizabeth]

I'm not sure how to obtain radial distance. In my lab all we were given was this toroid, with a given inner radius. from the inner radius, we used a linear track to move the hall probe out of the toroid every 5 cm. so for example, at 5 cm from the inner toroid, the B-field strength was 5.25. How would u convet 5 cm to radial distance if that's all that we have?

 

[UltrafastPED]

Make a drawing of the setup:

(a) Show the line of the linear track, this will be the X axis.
(b) The zero point for the linear track, which is the origin of the X axis.
(c) Locate the toroid with respect to the linear track.

A drawing is required for any experimental report; it shows how the experimental measurements are to be interpreted. If your notes are not adequate for the construction of this diagram the experiment will need to be repeated. Using this diagram:

The perpendicular distance from the linear track to the center of the toroid is Y', its Y coordinate.
The location where this perpendicular crosses the line of the linear track is X', its X coordinate.
The center of the toroid is (X',Y').

Each of your magnetic field measurements provides an X coordinate; the corresponding Y coordinate is zero because all of the measurements took place on the linear track.

So each of your magnetic field readings will be of the form MF=(something) at point (X,0).

The radial distance from the center of the toroid is calculated via the Pythagorean distance formula for rectangular coordinates. You can subtract the inner radius of the coil if the distance required is from the surface of the coil.