Investigating Ampere's Law for a Long Current Carrying Wire

One of the classes of problems dealing with magnetic fields concerns the production of a magnetic field by a current-carrying conductor or by moving charges.  It was Oersted who discovered back in the early 1800's that currents produce magnetic effects. The quantitative relationship between the magnetic field strength and the current was later embodied in Ampere's Law, an extension of which made by Maxwell is one of the four basic equations of electromagnetism.
 
PocketLab, used in conjunction with a long, straight current carrying wire, offers a great opportunity for students to quantitatively study the relationship between magnetic field strength B and (1) the current i in the wire and (2) the distance r from the wire's center.  Students will be able to confirm the experimental results that
bformula1
The picture below shows the experimental setup used by the author.  A long, straight wire (red) is strung from a ring stand to the floor, and the loose ends of the wire are attached to a DC power supply that allows varying the current as desired.  The current value is shown in amperes in the right-most digital display on the power supply.  The table allowed pulling the sections apart so that the wire could be in the center of the table.  The wire could just as well have been placed along the outer edge of the table.  A ruler is placed on the table zeroed at the center of the wire.  PocketLab can then be placed at the desired distance from the wire.
Experiment%20Setup2
The figure below shows a close up of PocketLab, the NSTA ruler, and the wire.  The ruler is zeroed on the center of the wire, and PocketLab is shown with its left edge at the 3 cm mark on the ruler.  Since PocketLab's magnetic sensor is located about 0.5 cm in from the left edge, shown by the black X drawn on PocketLab, the distance r from the wire in this photo would be 3.5 cm.  PocketLab is set to provide magnetic field magnitude data and is zeroed when there is no current in the wire.
Measuring%20Distance%20from%20Wire3
VARYING CURRENT WHILE KEEPING DISTANCE CONSTANT
 
The video below contains data for magnetic field magnitude while varying the current, but keeping the distance r constant at 1.5 cm throughout.  Data from this video or the attached magnetometer file can be used in Excel to obtain a chart of B vs. i.
The author's Excel chart below clearly shows that the magnetic field B is directly proportional to the current i in amps.  The linear trend/regression fit provides an R-squared value of 0.9999.  It is seen from the linear regression equation that the magnetic field increases by about 7.3 microT for each ampere increase in current.
constantdistance5
VARYING DISTANCE WHILE KEEPING CURRENT CONSTANT
The video below contains data for magnetic field magnitude while varying the distance, but keeping the current constant at about 6 amps throughout.  Data from this video or the attached magnetometer file can be used in Excel to obtain a chart of B vs. r.
The author's Excel chart below clearly shows that the magnetic field B is inversely proportional to the distance r in cm.  The power trend/regression fit provides an R-squared value of 0.9981.  It is seen from the power regression equation that the power is -1.072, very close to the -1 expected for an inverse first-power proportionality.
constantcurrent7

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