Physics 220 Laboratory: Magnetic Forces and Currents

Introduction

In this laboratory we will be testing the validity of the Lorentz force law which tells us how electric charges are affected by electric and magnetic fields:

F = q [ E + v × B ] .                                                              (1)

For the case when there is no net electric field present we just have that

F_B = q v × B .                                                                    (2)

|F_B| = q |v| |B| sin(θ) ,                                                               (3)

with the direction of the force determined via the right-hand rule. 

In terms of current in a wire, I, we can rewrite the magnetic force using q v = I L where L is a length of wire in the magnetic field and the vector, L, points in the direction of the current along the wire.  We therefore find that the magnetic force on a current-carrying wire is

F_B = I L × B ,                                                                    (4)

and also that

|F_B| = I L |B| sin(θ) ,                                                                 (5)

with the direction of the force determined via the right-hand rule. 

Apparatus

The apparatus provided can measure the force on a length of a current-carrying wire in a magnetic field set up by two magnets.  The power supply provides a current that can be varied from –4 amperes to +4 amperes by changing the current dial on the power supply and by reversing the red and black wires to the power supply. 

The magnetic field is provided by two rare earth magnets and the North and South poles of the magnetic configuration is lined up with the N (at 0 degrees and the star: *) and S (at 180 degrees) on the paper dial beneath the cup.  This configuration allows you to change the orientation of the magnetic field with respect to the current-carrying wire.  The net magnetic force from Eq. (5) is due to the horizontal length of wire, L, in the magnetic field.

This force is measured via Newton’s third law as the force that the current-carrying wire pushes/pulls back on the magnet-and-cup system.  This force is measured by the digital balance as the new mass of the magnet and cup, M'.  Therefore, the difference between the new mass and true mass is the effective mass due to the magnetic force:

m_e =   M' – M

and the force due to the current-carrying wire is then just F_B = m_eg which can be either positive or negative (up or down). This force is in newtons when the mass is provided in kg.

WARNING: Do not leave the magnet and cup configuration on the digital balance when you are not performing the experiment.  The digital balance is extremely sensitive and leaving the mass on the balance longer than you need to, or in between experiments, can affect the digital balances and therefore your experimental results.

A. Determine |B| and linearity of |F_B| with the current, I.

1. Verify with the compass provided that in the horizontal plane of the magnets, the North pole of the magnetic configuration is aligned with the star and 0 degrees on the paper dial beneath the cup. 

2. There are three lengths of wire in the magnetic field of the magnet: two vertical and one horizontal.  Why are we only considering the length, L, of the horizontal length of wire?  Use Eq. (4) to justify your result.

3. Determine from Newton’s third law which direction of the current makes m_e > 0 and m_e < 0.

4. Measure with a Vernier caliper the horizontal length of wire that will be in the magnetic field of the magnet configuration.

5. Place the magnet and cup system on the digital balance and orient the digital balance so that the horizontal length of wire is in between the two magnets.  Orient the wire such that the horizontal length of wire is perpendicular to the magnetic field.  Zero out the digital balance and then turn on the power supply.  Adjust the current to +4 amperes and note the reading on the scale.  In your Excel spreadsheet record the current and the effective mass due to the magnetic force on the wire.  Reduce the current in 0.5 amperes steps until the current equals zero.  Once the current is zero, swap the red and black wires that go into the power supply.  This will allow you to send a current in the opposite direction in the wire.  Now continue to decrease the current by 0.5 ampere steps until the current is –4 amperes.

6. Once you have done so, turn off the power supply and return the black and red wires to their original locations.  Also remove the magnet-and-cup configuration from the digital balance.

7. Use your spreadsheet to calculate F_B from m_eg.  Both should be in newtons.  Also use your spreadsheet to calculate IL (in Ampere-meters), which is the magnetic force divided by the magnetic field.  Plot m_eg vs. IL.  Add a trend line (best-fit line) to the graph and add the equation to the chart. Use the linest command in Excel (see page 67 for a refresher on Excel) and report the slope and intercept to 90% confidence.  What is the slope and what is the intercept?

B. Validate the sin(θ) Dependence of the Magnetic Force

1. Place the magnet and cup system on the digital balance and orient the digital balance so that the horizontal length of wire is in between the two magnets.  Orient the wire such that the horizontal length of wire is parallel to the magnetic field.  This corresponds to an angle of zero degrees.  Zero out the digital balance and then turn on the power supply.  Adjust the current to +4 amperes and note the reading on the scale.  In your Excel spreadsheet record the angle and the effective mass due to the magnetic force on the wire. Adjust the angle of the magnet so that the angle between the wire and the magnetic field is now 30 degrees. Again note the reading on the scale for this angle.  Repeat for angular steps of 30 degrees until you get to 360 degrees noting the reading on the scale and angle.

2. Use your spreadsheet to calculate F_B from m_eg.  Also use your spreadsheet to calculate I L |B| sin(θ).  Plot m_eg vs. I L |B| sin(θ).  Note that Excel expects angles to be in radians and hence you must use θ*PI()/180 for the angle.  Add a trend line (best-fit line) to the graph and add the equation to the chart. Use the linest command in Excel and report the slope and intercept to 90% confidence.  What is the slope and what is the intercept?  What does this slope and intercept tell you?  What would you expect the slope and intercept to be for what is plotted?

3. Use your spreadsheet to plot m_eg vs. θ, where θ can be in degrees.  What is the shape of the graph?