Induced e.m.f. (ε) = -NAdB/dt
Procedures:
A. Rate of change of magnetic flux
- A square solenoid was connected to a signal generator through an a.c. ammeter.
- 10 turns of a copper wire were winded tightly around the middle of the solenoid and the wire was connected to a CRO.
- The signal generator was turned on and set to 1 kHz. The CRO setting was adjusted to display a whole trace on its screen.
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The time base of the CRO was switched off. The length of the vertical trace shown on the CRO was recorded, which represented the induced peak-to-peak e.m.f. (ε) in the copper coil.
- Steps 3 to 4 were repeated with the other values of the frequencies (f) of the signal generator to 6 kHz in steps of 1 kHz. The current through the square solenoid was kept constant by adjusting the voltage output of the signal generator. The results were tabulated.
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A graph of the induced e.m.f. (ε) against the number of turns (N) was plotted.
B. Number of turns of coil
- Steps 3 to 4 were repeated with the other values of numbers of turns of the copper coil around the solenoid. The results were tabulated.
- A graph of the induced e.m.f. against the number of turns was plotted.
C. Cross-sectional area of coil
- Two square solenoids of different cross-sectional areas were connected in series to the signal generator. The solenoids both had the same number of turns per unit length but one had a larger cross-sectional area than the other.
- 10 turns of the copper wire were wired tightly around the middle of each solenoid. One copper wire was connected to channel 1 of a dual trace CRO and the other to channel 2. The solenoids were kept well apart from each other.
- The signal generator was turned on and set to 1 kHz. The CRO setting was adjusted to display both whole traces on its screen.
- The time base of the CRO was switched off. The length of the vertical trace shown on the CRO was recorded, which represented the induced peak-to-peak e.m.f. in the copper coil for each solenoid.
D. Orientation of magnetic field
- 10 turns of the copper wire were winded on a magnetic field board. The copper wire was connected to the signal generator through the a.c. ammeter.
- An axial type search coil was connected to the CRO and vertically put at the centre of the copper coil.
- The signal generator was turned on and set to 1 kHz. The CRO setting was adjusted to display the whole trace on its screen.
- The time base of the CRO was switched off. The induced peak-to-peak e.m.f. in the search coil was observed.
- The search coil was tilted. The changes of the induced e.m.f. shown on the CRO were observed and described.
Observation: An increase in the angle of tilting between the magnetic field board and the search coil leads to an increase in the induced e.m.f. observed.
E. Flux cutting and flux linking
- The small square was inserted completely inside the large solenoid.
- The large solenoid was connected in series to a d.c. power supply through a d.c. ammeter, and a rheostat.
- The small solenoid was connected to a light-beam galvanometer.
- The d.c. supply was turned on and set to 3A.
- The small solenoid was pulled out of the large solenoid. There was an induced current through the small solenoid. The small solenoid was moved at a uniform speed to keep the reading of the light-beam galvanometer constant. The reading of the light-beam galvanometer was recorded.
Current (I) = 2.4A
- The time taken for the complete removal of the small solenoid from the large solenoid was measured and recorded by a stop watch. The procedures were repeated 4 times and the mean time was taken.
- Steps 18 to 21 were repeated. The current through the large solenoid was reduced by adjusting the resistance of the rheostat. There was also an induced current through the small solenoid. The reading of the light-beam galvanometer should be kept constant at the value as in step 22.
- The time taken for the current through the large solenoid reduced to zero was measured and recorded by the stop watch. The procedures were repeated 4 times and the mean time was taken.
Results and Discussion:
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The rate of change of magnetic flux, the number of turns of coil and its cross-sectional area are directly proportional to the induced e.m.f. (ε). An increase in the magnitude of each of these three factors will lead to an increase in the induced e.m.f. (ε).
- The coils should be wound around the middle of the solenoids. It’s because the magnetic field in the middle of the solenoids is uniform and maximum.
- The maximum induced e.m.f. can be produced when the plane of the search coil is placed at the centre of the copper coil and at right angles (90 degrees) to the magnetic field board.
- From the results in steps 23 and 25 in Part E, it can be concluded that the induced e.m.f. is directly proportional to the rate of change of magnetic flux, i.e. a steady induced e.m.f. will result in a steady rate of change of magnetic flux.
- The solenoids are placed perpendicular to each other because this ensures that the magnetic field produced in each of the solenoids is not affected by that in the neighboring solenoids.
- Sources of error:
-There is reaction time of an individual.
-A stopwatch which is fast.
-The surrounding magnetic field of the neighboring solenoids may affect the experimental result.
-The setting and calibration of the CRO is wrong.
Suggested improvements:
-Repeat the experiment several times and take the average data for calculation.
-The time measured by a stopwatch is checked using another watch.
-Place the neighboring solenoids perpendicular to each other.
-Reset the setting and calibration of the CRO.
Conclusion:
From the experiment, it is observed that the factors affecting the e.m.f. induced in a coil due to a varying magnetic field in a neighboring coil are the rate of change of magnetic flux, the number of turns of coil and the cross-sectional area of coil.