Magnetic Flux of a Current Carrying Wire

Introduction

This experiment determines the field strength of a magnetic field by observing the force it exerts on a current-carrying wire. This surprisingly simple experiment works by creating a magnetic field by using permanent magnets. A wire is connected to a power supply and the force on the wire is measured using simple kitchen style electronic scales. Weight is actually a force, so it is easily measured using kitchen scales. But what about the force due to the weight rather than the magnetic field, how do we ignore that? Easy, we zero the kitchen scales when it is only holding the magnet.

The objective

To find how the strength of a magnetic field due to a wire varies with the current through the wire.

The apparatus

You will need:

• A power supply

• Copper wire

• Digital kitchen-type scales with zero function

• Multimeter

• Wires and crocodile clips

• Two magnets in a U-shaped yoke

• Wooden mounting blocks

This shows the scales with the two magnets held in a U bracket on the measuring pad of the scales. The current carrying wire passes through the U between the two magnets. One end of the wire is connected to the ammeter. The other end of the wire is connected to the power supply. The circuit is completed by the ammeter being connected to the supply.

The power source is connected in series with an ammeter and a copper wire.

The copper wire is supported between an arrangement of magnets in a U-shaped yoke, which provides a close approximation to a uniform field. The yoke containing the magnets sits on the scales, which measure the force on the yoke from the magnetic field.

The variables

The independent variable is the current. The dependent variable is the strength of the magnetic field as measured by the scales.

The Physics

The force on a single charge q moving at speed v due to a magnetic field B at right angles to the movement of the charge is given by:

F = qvB

If there are n charges per unit volume in our wire of length L and cross-sectional area A, then the total number of charges N is given by:

N = nLA

Therefore, the total force will be given by:

F = NqvB = nLAqvB

The current in a wire i is given by:

i = nqvA

This is substituted into the previous equation to give:

F =BiL

A schematic that shows the forces on the wire, the magnetic force upwards on the wire and the force due to gravity downwards.

Where B is the magnetic field, L is the length of the wire in the field (which is the length of the magnets), and i is the current. Therefore, the magnetic field is given by:

B = F/Li

When you plot the mass registered on the scales against the current, the gradient of your graph gives you a value for m over i. Consider forces on the wire. The force from the magnetic field upwards as measured by the scales is BiL.

The force downwards on the wire due to gravity is:

F = mg

The forces must balance, as the wire does not move; therefore:

BiL = mg

Therefore, the result for B is given by:

B = mg/iL

The gradient of the graph, mass against current, is m/I; substituting this into the previous equation gives you a value for the magnetic field.

The method

The electronic scales indicate the weight of the yoke and magnet assembly. We want to ignore this weight and concentrate on the force due to the current in the wire and the magnetic field. Zero the scales. The scales will now only show any additional weight due to the force from the interaction of the magnetic field and the current in the wire. Normally we would expect the wire to be pushed upwards, but the wire is being held rigidly in the two brackets on either side of the scales, so the force will press on the scales and cause a positive reading.

Switch on the power supply. With the power on, set the maximum current to a little over 5 amps. You should now adjust the voltage until the meter reads as close to 1 amp as you can get, as shown here:

This shows the power supply to deliver a maximum of a little over 1 amps, the voltage has been set to provide a current of 0.998 amps to the circuit.

Note the reading of the amps and the weight indicated on the scales. Now repeat this for currents of 2, 3, 4, and 5 amps.

The Video

Watch a video for the Magnetic Flux Density e-practical here.

This shows how to use it and how to collect the data.

The E-Practical

Perform the experiment yourself, collect your own data, make mistakes and be able to correct them. The e-practical requires that your browser can run WebGL 2 (usually found on Windows browsers, safari on iOS, and various Mobile browsers, test with https://get.webgl.org/webgl2/). This link is for students and evaluation only, schools should purchase a site licence.

You can zero the scales by clicking on the red zero knob.

You can switch on the power supply by clicking the red on/off button on the supply.

The length of the wire is 8.5 centimeters.

Try it yourself

The Results

Complete this table of results:

Plot a graph of m against i and calculate the gradient. Use the formula given in the Physics section to calculate the strength of the magnetic field.

You should obtain a result of around 0.05 Tesla.

Further Discussion

Would the experiment work as well with a spring balance?

Justify your answer.

This section is adapted from material developed by Dr Robert Lucas and is related to the book High School and Undergraduate Physics Practicals, published by CRC Press.