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In the experiment, the Lorentz's law was studied. The law states that a charge q moving with velocity in a magnetic field experiences a force given by the equation. This equation implies higher velocity leads to big magnetic field and stronger force on the charge. In this experiment, the charge moved perpendicular to the magnetic field hence was used to obtain the maximum possible values.
To study Lorentz's law in relation to the current flowing in the wire, the magnetic field surrounding the wire and the length of the wire immersed in the field. This consisted of three investigations which involved the study of the magnetic force of short current carrying wire that was immersed in a magnetic field as shown in the figure below.
Investigation 1: Dependence of Force on Current
With no current no current flowing in the wire, the armature was balanced and the power supply, wire loop and the ammeter were connected in series. The magnet assembly was aligned with the value 50 on the lower scale and the length L of the wire recorded. The writer was moved to a scale x=10 and the current increased until the armature was set back to the level. The current and the rider opposition were recorded and a similar procedure was repeated for other scales until the end of the scale and then back to 10mm reading. The obtained data was recorded in the table below.
From the data, it was found the two measurements obtained at the same position differ. This difference was due to an error that was found obtaining the midpoint between the two current values at each point. The graph was found to show a linear relation between distance and current as implied by the F=ILB. Using the information above, the magnetic field was calculated as follows.
Investigation 2: Dependence of Force L', the Length of Wire in the Magnetic Field
The length L of the wire that immersed in the magnetic field was varied by moving the magnetic assembly from the brass wire loop. This was done until the rear edge of the magnet assembly coincided with a 50 mm value on the lower scale. The rider was set to x=70 mm and the current adjusted until the armature wire was in horizontal position. The current was held constant and the magnet assembly moved in steps of 5 mm along the y direction until the whole conductor was out of the magnetic field. The rider was moved to re-level the armature for every movement and its position x was recorded giving rise to the table below.
From the graph above, it is evident that the error bar is very small thus the slope error is considered to be insignificant. Using a similar approach as in investigation I, the magnetic field was calculated as follows.
Investigation 3: Dependence of Force on the Strength of the Magnetic Field B
The balance was set as in investigation 1 whereby the magnet and the rider were set at 5O mm and x=70 respectively. The current was adjusted to find a horizontal position and the position of the rider was recorded. The current was switched of and one of the five magnets removed. The power supply was then set to the same value for the five magnets and the rider moved until the armature was in level. The position was recorded and the procedure repeated until all the magnets were removed. The obtained readings were entered in the table below. Using the data in the table above, the following graph of x vs. number of magnets was plotted.
As observed from the graph the straight line does pass through the origin which might be due to an offset in the length of the wire.
The objectives of the experiment which was to prove the Lorentz's Law which states that a charge q moving with velocity in a magnetic field experiences a force given by the equation: which implies that the faster the velocity of the charge, the bigger the magnetic field, and the stronger the force in the charge was achieved. Although human error was obtained in the first investigation, it was proved that the same magnetic field was always obtained irrespective of the charge. The linear relationships in all investigations' graphs showed that x increased with the increase in the number of magnets, length and current.