Last Name: 
CID:           

Note: Items in red are measurements that must be made as you do the experiment.

Introduction

You have learned that the Lorentz Force on a moving charge in a magnetic field is given by the equation:   Eq. 1 When current flows in a wire, charges move in the wire, and a force is exerted on each charge as it moves. We can add the forces on all the charges to get the force on the entire wire. With a little algebra, we can show that the force on a wire of length L carrying a current i in a uniform magnetic field B is given by the equation: Eq. 2 where the direction of L is the direction current flows through the wire.

Figure 1

Using Eq.2, determine the direction of the force on the wire in this experiment. The cross product has a sin θ (theta) in it. What is the value of θ (theta) for this experiment?

There is one complication, however, that we must consider. In our experiment, B is not constant. We do know, though that we can calculate the force on every tiny segment of  the wire (each with length dx) and add up all the results. That is:

Finally, we must multiply this by the number of turns in the coil of wire, N. This gives us the result:

  Eq. 3

where C and D are the ends of the wire segment shown in Fig. 1 above.

Using the Hall probe:

In this lab, you will use a very sensitive device called a Hall probe to measure the magnetic field B between the poles of a  strong magnet.  The Hall probe produces a voltage that is proportional to the magnetic field. We can convert the voltage reading of the Hall probe to magnetic field using the relation B = (2 Tesla/Volt) V. That is, when V = 2 mV, B = 4 mT. You must orient the semiconductor strip on the tip of probe correctly, as only the component of B perpendicular to the strip is measured. This strip is in small metal frame that can be fixed in either of two positions. If you think of the strip as a little window, then magnetic field lines must pass through the strip as light passes straight through a window.

Experiment:

1.   Measure the magnetic field strength at 1 cm intervals along the wire and plot these values on the grid. Note that you should let Point C (Fig. 1) be 0.0 cm. 2.      Graphically evaluate the integral of Eq. 3 by measuring the the area under the curve you made in Step 1. (Note: one grid square = 1 x10-4 Tm). (Do not multiply by Ni yet!)       Enter the value of the integral :   Tm (Use the form 1.23E-4, etc.) 3.      Calculate the expected force on the N = 500 turn coil due a current of i = 300 mA (=0.300 A) by using Eq. 3.       Calculated value of F:  N   4.      Adjust the power supply so that I = 300 mA is flowing through the wire coil, and measure the resulting magnetic force using the balance.  Be sure to subtract the weight of the coil which can easily be measured at i = 0. Recall that Fg = mg.      Measured value of F:  N

5. Show that the magnetic force on the coil is proportional to the current flowing through it by repeating Step 4 with two additional coil currents: 100 mA and 200 mA. For each measurement, divide the force by the current. By Equation 3, these answers should be the same.

        F₃₀₀/I₃₀₀ :    N/A
        F₂₀₀/I₂₀₀ :    N/A
        F₁₀₀/I₁₀₀ :    N/A

Calculate the % difference between the largest and smallest result. Use 100*(Large-Small)/Large

       Percent difference:    %