The search coil is always used to measure the magnetic fields. It consists of N turns of the coil enclosing an area A. When exposed to a changing magnetic field B, an e.m.f. is induced across the ends of the coil. The induced e.m.f. (ε) is directly proportional to the rate of magnetic field, i.e. ε = －NA dB/dt .When the search coil is connected to a CRO, the corresponding induced e.m.f. and hence magnetic field magnitude can be determined.
Precautions for magnetic field around straight wire
1. The wire should be long
2. The distance(r) should much smaller than the length of the wire.
Procedure
A. Magnetic field around straight wire
1. The circuit as shown in Fig.C15.1 and a lateral type search coil to a CRO was connected.
2. The signal generator was turned on and was set to 0.5A and 5kHz.
3. The centre of the search coil was placed 1 cm away from the straight wire. The search coil was at the same level and perpendicular to the straight wire. The CRO setting was adjusted to display a whole trace on its screen.
4. The time base of the CRO was switched off. The length of the vertical trace shown on the CRO was recorded, which represents the induced peak-to-peak e.m.f. (V) in the search coil and also the magnetic field around the straight wire.
5. The steps 2 to 4 were repeated with the other values of current (I) from the signal generator in steps of 0.1A. Then, the results were tabulated.
6. A graph of the induced e.m.f.(V) against the current(I) was plotted.
7. The steps 2 to 4 were repeated with the others values of distances (r) of the search coil away from the straight wire. The results were tabulated.
8. A graph of the induced e.m.f.(V) against the reciprocal of distance() is plotted.
9. The frequency of the signal generator was varied to change the sensitivity of the search coil.
B. Magnetic field around slinky solenoid
10. The circuit as shown in Fig.C15.2 and a lateral type search coil to a CRO was connected. The stretched length of the solenoid is 1 m.
11. The signal generator was turned on and was set to 0.5A and 5kHz.
12. The search coil was placed at the centre of the solenoid. Make sure that the search coil was perpendicular to the solenoid. The variation of induced e.m.f. was shown on the CRO.
13. Step 12 was repeated with placing the search coil at the end of the solenoid, across its cross-section and along its length.
14. The search coil was placed at the centre of the solenoid again. The time base of the CRO was switched off. The length of the vertical trace shown on the CRO was recorded, which represents the induced peak-to-peak e.m.f.(V) in the search coil and also the magnetic field around the solenoid.
15. Step 14 was repeated with the other values of currents (I) from the signal generator in steps of 0.1A. The results were tabulated.
16. A graph of the induced e.m.f.(V) against the current (I) was plotted.
17. Step 14 was repeated with the other stretched lengths (l) of the solenoid. The space between coils must be even. The results were tabulated.
18. A graph of the induced e.m.f.(V) against the reciprocal of the stretched length of the solenoid(1/l ) was plotted.
Results
A. Magnetic field around straight wire
The sensitivity of the search coil can be increased by increasing the frequency.
B. Magnetic field around slinky solenoid
When placing the search coil at the centre of the solenoid, across its cross-section, the induced e.m.f. shown on the CRO, i.e. the length of the vertical trace is the maximum, that means the magnetic field of the straight wire is the maximum.
When placing the search coil at the end of the solenoid, across its cross-section, the induced e.m.f. shown on the CRO, i.e. the length of the vertical trace is nearly half that at the centre of the solenoid, that means the magnetic field of the straight wire is nearly half that at the centre of the solenoid.
When placing the search coil along the length of the solenoid, the induced e.m.f. shown on the CRO is quite uniform except near its two ends.
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Discussion
1. From the V-I graph in step 6 (Graph A.1), the current flowing in the straight wire is directly proportional to the induced e.m.f. (V). As the induced e.m.f. ε = －NA dB/dt, the current flowing in the straight wire increases with the magnetic field produced by the current-carrying straight wire.
From the V- graph in step 8 (Graph A.2), the distance from the straight wire is inversely proportional to the induced e.m.f. (V). As the induced e.m.f. ε = －NA dB/dt, the distance from the straight wire decreases with the magnetic field produced by the current-carrying straight wire.
Thus, the result agree with the equation , where μ0 is the permeability of free space.
2. From the V-I graph in step 16 (Graph B.1), the current flowing in the slinky solenoid is directly proportional to the induced e.m.f. (V). As the induced e.m.f. ε = －NA dB/dt, the current flowing in the slinky solenoid increases with the magnetic field produced by the current-carrying solenoid.
From the V- graph in step 18 (Graph B.2), its stretched length is inversely proportional to the induced e.m.f. (V). As the induced e.m.f. ε = －NA dB/dt, its stretched length decreases with the magnetic field produced by the current-carrying solenoid.
Thus, the result agree with the equation , where μ0 is the permeability of free space and is the number of turns of the solenoid.
3. It is necessary to place the search coil at the same level and perpendicular to the straight wire. Otherwise, the magnetic field cannot cut the search coil completely and ideally. Then, the induced e.m.f. is not the maximum and even there is no induced e.m.f. shown on the CRO. As a rollecteesult, the data cd is not accurate.
4. There are several sources of error. First, there is reading error, zero error of ammeter. Secondly, the space between coils is not even. Thirdly, the magnetic field around the straight wire and the slinky solenoid is easily disturbed by other apparatus nearby. Finally, the search coil is not at right angles to the straight wire and the solenoid, this make the data collected becomes inaccurate.
To avoid disturbance, the set-up should be significantly distant from the return leads and other apparatus. The space between coils is nearly even. The search coil is nearly at right angles to the straight wire and the solenoid Therefore, the experiment can be improved.
5. Reason for the sensitivity of the search coil can be increased by increasing the frequency.
First of all, the search coil detects a varying B-field through the current induced in it which is:
From the deduction, we can see that with A and B0 held constant, which are the area of search coil and the peak value of the varying B-field respectively, the rate of change of magnetic flux Φ increases with increasing ω which is the angular frequency with value 2πf, where f is the frequency of the B-field.
6. The Earth’s field can be ignored because it is a steady magnetic field.
Conclusion
The magnetic field around a long straight wire carrying a current is directly proportional to the current (I) and inversely proportional to the distance(r) from the wire. The magnetic field inside the solenoid carrying a current is directly proportional to the current (I) and the number of turns (N) but inversely proportional to the length (l ) of the solenoid.
