The value of the constant μo, which is called the permeability of free space, is
4π × 10-7 H m-1.
Procedure
The circuit was set up as shown below.
The signal generator was set to 5 kHz. The CRO was adjusted such that a trace was displayed. The frequency was changed to find out how the trace on the CRO was affected. The output of the signal generator was adjusted to produce a current. The time base was switched off and the length of the vertical trace on the CRO was measured. Steps were repeated by using increasing current. The centre of the search coil was placed 1cm away from the wire. CRO was adjusted such that the vertical trace occupied the full height of the screen. The distance of the search coil from the wire was increased in steps and the length of the vertical trace on the CRO was measured. The result was then tabulated.
Results
Signal generator frequency f = 5000Hz
Discussion
Having done the series of experiments, we can conclude that magnetic field B at a point near a long straight wire is directly proportional to the current I in the wire and inversely proportional to the distance r from the wire.
This conclusion can be drawn as the graph of l against I is a straight line and l is almost directly proportional to I in the presence of experimental errors. Due to the fact that l is proportional to induced emf in the coil and the field strength, magnetic field is directly proportional to the current. Also, the graph of l against r shows that I is inversely proportional to r. Therefore, magnetic field is inversely proportional to the distance from the wire.
In this experiment, several precautions should be taken. For one thing, the alternating current should be increased gently from zero. Otherwise, the a.c. ammeter would be over-deflected which may cause damage to the ammeter. Secondly, the ends of PVC covered copper wire should be twisted. Otherwise, there may be induced emf induced by that part of the copper wire which may affect the result obtained. Thirdly, there should be only one unique changing factor that affects the result. That means the distance r form the wire or frequency should not be varied when investigating the relation between current and length of CRO trace. Fourthly, the area of the search should be small so that it has greater spatial resolution.
Indeed, there are errors in this experiment. To begin with, the search coil may not be put at the same level of the wire. If there is inclination between the search coil and the wire, there will be a component of the magnetic field formed. The horizontal component of the magnetic field will be measured. This is not the maximum magnetic field that we want. The face of the coil should be perpendicular to the field produced by the current in the wire.
In addition, there are errors produced by moving the coil to investigate relation between r and l. This is because the coil is not moving along the same line when varying the distance r from the wire. Also, reading error is engendered when reading the mark of ruler, trace of CRO and ammeter. Furthermore, there were other electrical appliances which produced changing magnetic field and the result of the trace of CRO thereby was affected.
Improvement could be made to increase the accuracy of the experiment. First, the sensitivity of search coil should be increased by increasing the frequency. The more frequent the voltage change across the wire, the more frequent is the change of the magnetic field. The magnetic field across the search coil is proportional to the sensitivity. Second, the search coil should be rotated to obtain the maximum value of the magnetic field to ensure the field is perpendicular to the coil. Third, the set-up should be placed well away from the stray fields such as those from main sockets.