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Magnetic Field on a Current Loop's Axis

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Submitted by Rich on Wed, 05/02/2018 - 17:13

Introduction

In this lesson students will find that a current-carrying loop can be regarded as a dipole, as it generates a magnetic field for points on its axis.  Students use PocketLab Voyager and Phyphox software to compare experiment and theory for the magnetic field on the axis of a current loop.  A similar experiment not making use of Phyphox can be found by clicking this link.  An experiment making use of a magnet, instead of a current loop, can be found by clicking this link.

There are many ways that you can make a current loop.  The author used a plastic ribbon spool approximately 3" in diameter and 3/4" wide, and then wrapped 10 turns of insulated wire around the spool.  The ends of the wire were connected to a DC power supply that supplied constant current for the current loop.  Figure 1 shows Voyager with its magnetometer centered on the axis of the spool.  Voyager's magnetic sensor is located almost directly below the letter Z on the circuit board inside Voyager.  It is important to keep the magnetic sensor on the loop axis while it is moved to known distances from the center of the loop. Voyager is attached to the end of a balsa stick that can be kept parallel to the axis of the current loop . 

Magnetic current loop setup
Figure 1

Phyphox Software

Phyphox (physical phone experiments) is a free app developed at the 2nd Institute of Physics of the RWTH Aachen University in Germany.  The author of this lesson has been working with a pre-release Android version of this app. It supports BLE (Bluetooth Low Energy) technology to transfer data from multiple Voyagers to the Phyphox app.  A public Android beta release of the Phyphox app is now available.  

The experiment of this lesson is in a file named CurrentLoop.phyphox and it accompanies this lesson.  This file can then be opened in Phyphox and will appear in the PocketLab Voyager category of the main screen, similar to that in Figure 2.

Current Loop Axis Magnetic Field Theory

Figure 2 shows a diagram and the equation for the magnetic field B on the axis of a current loop.  Derivation of this equation requires knowledge of the Biot-Savart Law, calculus and trigonometry.  But in this lesson we are interested only in comparing experimental results from Voyager's magnetometer to the theoretical equation in Figure 2.  If desired, AP and college students can also consider derivation of the equation.  The author's setup used a current of i = 5.1 amp, R = 0.0361 m, and a loop with 10 turns of wire.

Magnetic current loop theory
Figure 2

See the file CurrentLoop.pdf for a detailed step-by-step procedure and discussion of experimental results.  Here is a short video that explains how this experiment is done:

Magnetic Field on a Current Loop's Axix
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