LAB 4: MAGNETIC FIELD AND CURRENTS: AN AMMETER 271

Part 3: Circuit model of surface resistivity

Solder at least 25 identical resistors in a square mesh as shown in Fig.L3.2b. (A lab technicianor the instructor may do this ahead of time for you.) This is a circuit model of a thin layer ofresistive material. Imagine you insert a current at a point in the middle of the mesh. Drawthe current paths. What do they look like as the mesh becomes finer and larger?

L3.8. Using an ohmmeter, measure the resistance between adjacent points, such as A and B,at different places across the mesh (i.e. in the center and closer to the edges). What resistanceare you expecting to approximately measure in the middle of the mesh based on your prelabproblem PL3.4?

L3.9. How do your measurements compare with the calculation for different pairs of adjacentpoints across the mesh?

L3.10. If you have time and you are interested, repeat measurements and calculations forproblem P11.16. How would you make a discrete model for volume, not surface, resistivity?

Conclusions:

1. Resistivity and surface resistivity can be measured using a four-point probe voltage andcurrent measurement. The calculation of the resistivity from this measurement is basedon superposition of two currents.

2. The method of measurement is slightly different for thick samples and thin layers, as wellas for high-resistivity and low-resistivity (high conductivity) materials.

3. We can make a circuit model (mesh of identical resistors) of homogeneous resistive layersas well as resistive blocks of material. To calculate the value of resistance between any twopoints in the circuit model, we can use the two-point probe analysis based on superpositioninstead of a relatively complicated circuit analysis.

Lab 4. Magnetic field and currents: an ammeter

Background:Circuits, Chapter 12 in Introductory Electromagnetics

A current produces a magnetic field, which can in turn produce a force on either a magnet oranother wire with current flowing through it. In this lab, we will produce a static magneticfield with a dc current flowing through a dense spiral winding, usually called a solenoid. Themagnetic force will act on a small magnet (a compass needle). By measuring the force on thesmall magnet, we can measure the intensity of the current flowing through the solenoid.

Purpose: to see how current produces a magnetic field, and to learn how to measure thecurrent by measuring magnetic force. The purpose of this lab is to make a simple instrument,to learn how to calibrate it and extend its operating range, and to understand its limitations.

Pre-lab problems:

PL4.1. A circular current loop of radius a is positioned in the xy plane, centered on the zaxis, Fig. L4.1. Use the Biot-Savart law to find the expression for the magnetic flux densityvector along the z axis.

272 SIMPLE ELECTROMAGNETICS LABS

PL4.2. Find the magnetic force that acts on a small current element positioned on the z axisin the yz plane, making an angle of 45° with the z-axis (Fig. L4.l).

Lab:

Equipment and parts:

- a dc power supply; a multimeter;

- a compass, insulated wire, two potentiometers.

z

Fig. L4.1. A circular current loop in the xy plane and a current element on the axis of the currentloop.

Part 1: Calibrating the ammeter

You can make an ammeter by winding insulated wire (about 30-40 turns) around a compass.Connect the ammeter as shown in Fig. L4.2a. The pot resistor is used in series with the powersupply and ammeter in order to limit the current. Set it to 50 n. You can measure the currenteither by inserting a commercial ammeter in series in the circuit, or by measuring the voltageacross the pot.

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Fig. L4.2. (a) Setup for calibrating the ammeter. (b) Setup for increasing the current range of theammeter.

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LAB 4: MAGNETIC FIELD AND CURRENTS: AN AMMETER 273

L4.1. Start with a low voltage (about 1 V) on the power supply, and slowly increase it. Youshould see the compass needle deflect as you increase the current through the solenoid up to acertain point. How do you orient the compass initially so that you measure the largest currentrange?

L4.2. In order to be able to use your ammeter, you need a scale. Draw the scale on a piece ofpaper by measuring known currents (this is what the commercial ammeter is for) and recordingthe compass needle deflection. What is the largest value of the current you can measure? Whatis the smallest nonzero current you can measureZ What is the sensitivity of your ammeter,i.e., how accurately can you measure small changes? Is your scale linear (it is linear if the"deflectionangle is linearly proportional to the current with some multiplication constant)? .

L4.3. Compare your scale with that of your classmates. How do they compare? How practicalis your ammeter for manufacturing?

..Part 2: Measurement of the earth's magnetic field

The earth is a large magnet and the initial position of the needle is determined by the earth's-magnetic field. (You can read more about this in Chapter 17 in Introductory Electromagnetics.)

L4.4. Determine the position of the compass that would allow you to have the needle deflecta known amount when the magnetic field generated by the current is equal to the earths'magnetic field. Measure the required current for this case.

L4.5. From the value of current obtained in L4.4 and your prelab homework PL4.1 results,determine the magnetic flux density that the needle is in. This is the value of the earth'smagnetic flux density at the place where the needle is located. What approximations do youhave to make when answering this question?

Part 3: Measuring larger currents (changing the current range)

L4.6. You have found that after the current is increased beyond a certain point, there is nofurther deflection of the needle (your instrument is saturated). Also, after some current level,you will burn the resistor that regulates the current. The setup shown in Fig. L4.2b can beused to measure larger currents. Explain how it works. Find the current h as a function ofthe resistor values Rl and R2.

L4. 7. Determine the values of Rl and R2 that allow you to measure a current range 3 timeslarger than the one you had in Part 1. Set the values of the pots to those you calculated andcalibrate a new scale. What is the smallest nonzero current you can measure? What is thesensitivity of your ammeter?

Conclusions:

1. A current produces a magnetic field. By measuring the torque of this field on a smallmagnet, we can measure the current.

2. Every instrument needs to be calibrated. The calibration is different for different rangesof the instrument.

3. The simple ammeter you made can be used to indirectly measure the intensity of themagnetic field of the earth at the place where the ammeter is located.