permeability of free space

Data Collection and Processing:

I → Current flowing through solenoid

B → Magnetic field strength

Raw Data Table showing magnetic field within a solenoid for a particular value of current flowing through it.

Graph of current passing through the solenoid vs magnetic field strength inside the solenoid

Slope of best fit line = -0.406 mT A-1

Maximum slope = -0.289 mT A-1

Minimum slope = -0.497 mT A-1

Thus, slope = -0.406 ±0.117 mT A-1

As we already know,    

Where B → Magnetic field strength

         → permeability of free space

        n → number of turns per unit length of solenoid

        I → current passing through solenoid

Number of turns in solenoid = 250

Length of solenoid = 10 cm = 0.1 m

Thus, n = 2500

From equation,  =  = slope of graph plotted = -0.406 ±0.117

                                                = -0.406 ±28.8 %  mT A-1

Thus,  -1.62 X 10-4 ±28.8% mT A-1

        = (-1.62 ±0.47) X 10-4 mT A-1 

Thus,  = (-1.62 ±0.47) X 10-7 T A-1

Conclusion:

The literature value for permeability of free space = 4π X 10-4  T A-1 

                                                       = 1.26 X 10-3  T A-1

Evaluation:

Weaknesses in the experiment:

• There were a number of electrical devices close to the solenoid. Each of theses devices, namely the laptop, LabPro, Power Pack and variable resistor had current carrying conductors. These created a magnetic field which interfered with the magnetic field of the solenoid.
• The magnetic field was not constant within  the solenoid.
• If the sensor is kept in one position, the background field of the earth will not affect the magnetic field strength.
• The sensor measures the component of the magnetic field that is perpendicular to the white dot on the end of the sensor tip.

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