# PHYSICS 2049L – Experiment #210: Magnetic Field & Electric Current

PHYSICS 2049L – Experiment #210: Magnetic Field & Electric Current
May 14, 2022

Objectives
1. Gain a better understanding of the relationship between electrical current in a conducting wire and magnetic fields.
2. Confirm the effect of using coils of wire to increase the magnitude of magnetic fields.

Magnetic Field due to a Current
In 1820, Hans Christian Oersted discovered that a current carrying wire produced a magnetic field. This discovery was the beginning of the discipline called electromagnetism. The experiment revealed that the magnetic field (B) produced was directly proportional to the current (I) and inversely proportional to the radial distance (R) from the wire.

Magnetic Field Formula for Current Carrying Straight Wire
When electric current is carried in a wire, a magnetic field is formed around it. The magnetic field lines form concentric circles around the wire. The magnetic field direction depends on the direction of the current. It can be determined using the “right hand rule”, by pointing the thumb of your right hand in the direction of the current. The direction of the magnetic field lines is the direction of your curled fingers.
The magnitude of the magnetic field (B) depends on the amount of current (I), and the distance (d) or (r) from the charge-carrying wire.

The formula includes the constant:
This is called the permeability of free space and has a value:
The unit of magnetic field (B) is the Tesla, (T).

B = magnetic field magnitude (Tesla, T)
= permeability of free space ( )
I = magnitude of the electric current (Amperes, A)
r = distance (m)

Magnetic Field Formula Example:
What is the magnitude of the magnetic field 0.10 m away from a wire carrying a 3.00 A current?
If the current has a vector direction out of the page (or screen), what is the direction of the magnetic field?

Answer: The magnitude of the magnetic field can be calculated using the formula:

Continuing,

In summary, the magnitude of the magnetic field is 6.00 x 10-6 T or (micro-Tesla).

The direction of the magnetic field can be determined using the “right hand rule”, by pointing the thumb of your right hand in the direction of the current. The direction of the magnetic field lines is the direction of your curled fingers. The current has a vector direction out of the page, and so your fingers will curl in the counterclockwise direction. This same characteristic is illustrated in the diagram on the first page. Therefore, the magnetic field lines point in the counterclockwise direction, forming circles around the wire.

Magnetic Field for Current Carrying Wire Coil
The previous section addressed the magnetic field for a current carrying straight wire and provided the equation for the magnetic field magnitude:

The formula for a current carrying wire coil will now be presented.

Summarizing, the magnetic field magnitude at the center of a coil with radius (R) is directly proportional to the magnitude of the current (I) and the number of wire coils (N). Increasing the current and/or the number of coils, will result in an increase magnetic field strength inside the coil.

Experiment Part 1 – Validate the Formula for Magnetic Field in a Current Carrying Wire
Utilize the app found at the link below to make measurements and complete the tables. Once you follow the link, click on the Embedded Link – “Magnetic Field from a Wire”. The app will launch. Click on the “Begin” button and you will enter the simulation tool for the Magnetic Field from a Wire Lab.
https://www.golabz.eu/lab/magnetic-field-from-a-wire
https://gateway.golabz.eu/os/pub/physicsaviary/FieldFromWire%25252Findex.html/w_default.html?scale=8840&height=690
This exercise involves setting the value of the current flowing within a wire (Amps), utilizing a measurement device to determine the magnetic field strength in Tesla (T), and moving the measurement device to various distances from the current carrying wire and recording the magnitude of the magnetic field in Tesla. You can click on the white boxes located on the top and bottom of the display to reveal controls and readings.
Step 1: Click on the “Current” button and set the current value to 2.4 A
Step 2: Click on the “Grid” button located on the top of the display to display the distance grid.
Step 3: Click on the “Field Strength” button to display the magnetic field magnitude measured. NOTE: It is displayed in μT or 1*10-6 T.
Step 4: Click on the “Location of Field Sensor” button to display controls for positioning the sensor.
Now proceed to make the measurements required to complete the table below. Ignore the sign (+/-) of the magnetic field strength measurement and just record the magnitude.
Then use the magnetic field formula to calculate the field strength and compare it with the measured value. Calculate the percent error between measured and calculated values.

Current
(A)

Distance
(m) Measured
Magnetic Field
(T) Calculated
Magnetic
Field (T)
Percent
Error
2.4 A .01 .0000474 .000048 1.25%
2.4 A .02
2.4 A .03
2.4 A .04
2.4 A .06
2.4 A .08

Step 5: Change the value of current to 8.9 A and repeat the measurements and calculations for the table below.

Current
(I)

Distance
(m) Measured
Magnetic Field
(T) Calculated
Magnetic
Field (T)
Percent
Error
8.9 A .01 .0001777 .000178 0.17%
8.9 A .02
8.9 A .03
8.9 A .04
8.9 A .06
8.9 A .08

QUESTION: From your measurements and calculations in the two tables above, what can you conclude regarding the behavior of the magnetic field for current carrying straight wires?

NAME___________________________
Experiment Part 2 – Validate the Formula for Magnetic Field in Current Carrying Wire Coils
This exercise will enable you to verify the formula for the magnetic field strength (B) in the center of a group of coils carrying current.

Where I, represents the current, N represents the number of turns or coils, R is the radius of the coil, and
.
Follow the link below and download the app – “Magnets and Electromagents”. If you have difficulty, use the second linke. Once the app has downloaded, launch it. It will launch with the Bar Magnet displayed. Click on the “Electromagnet” tab on the top to switch to the magnetic field wire coil display. Then follow the steps below.
Step 1: Configure the settings in the upper right control panel to be the same as shown below

Step 2: Set the Batter Voltage to 10 volts and place or move the Magnetic Field Meter such that the “cross hairs” of the sensor are located at the center of the current carrying coil.
Step 3: Record the magnitude of the magnetic Field (B) in the table below in Gauss (G).
Step 4: Utilize the control panel to increase the number of loops to “2”.
Step 5: Record the magnitude of the magnetic Field (B) in the table below.
Step 6: Repeat the previous two steps for the number of control loops being 3 and 4.
Number
of Coils
(N) Measured
Magnetic Field
(G)

1

2

3

4

QUESTION: Does the measured magnetic field strength behave as expected based upon the formula?

QUESTION: Does increasing the number of coil turns (N), cause the current in the wire to increase, decrease or remain the same?

APPENDIX
Here are the links utilized during the virtual lab today:
1. This link illustrates how magnetic field lines form in and around a magnet. The field lines exit from the North pole of the magnet and travel to the South pole where they reenter the magnet and flow straight through the magnet to the North pole, where they exit and repeat. By pressing the “Magnet ON” button, magnetic field lines become visible when the iron filings orient themselves to align with the magnetic field lines.
https://micro.magnet.fsu.edu/electromag/java/magneticlines/index.html

2. This link demonstrates how the magnetic field lines form around a magnet, exiting at the North pole and reentering at the South pole. Controls on the right side enable the user to modify the “Magnetic Field Strength”, flip polarity, see inside magnet, show field lines, show compass, show field measurement meter, and display the earth –with it’s internal magnet and field lines extending into space. Open the link below and download the app.

3. This link illustrates the relationship between the direction of the current flowing through a conducting wire (red arrow) and direction of the concentric rings of magnetic field that are generated by the current. The relationship is dictated by the “Right Hand Rule”. Align your right thumb parallel to the wire and wrap your fingers around the wire to indicate the direction of the magnetic field lines. The user can also drag/move the compass around the wire to indicate how the direction of the magnetic field changes as the compass traverses around the wire:
https://www.walter-fendt.de/html5/phen/magneticfieldwire_en.htm

4. This link enables the user to visualize the concentric magnetic field lines that form perpendicular to a wire with current flowing through it. The user can rotate the viewpoint and move along the wire to confirm the existence of the magnetic field rings throughout the length of the wire. Download the app from the site below:

5. This link This link enables the user to measure the magnetic field strength (B) around a single conducting wire while varying the current (I) flowing through the wire, and the distance (R) the magnetic measurement is taken from the wire: https://gateway.golabz.eu/os/pub/physicsaviary/FieldFromWire%25252Findex.html/w_default.html?scale=8840&height=690

6. This link allows the user to explore the magnetic field that results when a straight wire is turned into a coil and current flows through it. The user can increase/decrease the current flow by modifying the voltage across the coil. Further, the user can change the direction of the current flow, and hence the magnetic field direction, by changing the polarity of the battery voltage. Magnetic field lines can be displayed, compass can be dragged around the field, electrons (current) can be displayed, and a magnetic field meter can be activated to measure the field strength anywhere on the diagram. Finally, the number of coil turns can be varied from 1 to 4, to demonstrate the additive effect on the magnetic field strength when more coil turns are utilized. There is also the capability to use AC current in the model. The app can be downloaded from the site below. Just make sure to select the “Electromagnet” tab once the app launches:

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