Experiment No : EM 8 Experiment Name: Inductance of a Solenoid Objective: Investigation of the inductance of different solenoids and their dependence on certain parameters of solenoids Theoretical Information : If an electric current flows through a conductive wire and the current-carrying wire has a regular geometry, in another words it has a high symmetry, a magnetic field is created by the steady current flows through this wire (Amperé's law) and the magnitude of the magnetic field is proportional to the current. B.dl = 0.I 3. Where 0 is magnetic susceptibility which is a measure of the extent to which free space can pass through the magnetic field The direction of the magnetic field generated by the current passing through the conductor is determined by the right-hand rule. According to this rule, one can find the magnetic field direction by pointing right thumb in the direction of the current in the wire and curling the other four fingers. The fingers will be curled in the same direction as the magnetic field around the wire. In this experiment, we will deal with the magnetic field generated by the current flowing through the coils. This magnetic field varies depending on the current (I), the area (A) of the coil, the number of turns (N) of the coil and the length of the coil (). Magnetic field formed in the coil takes a simpler form if l r. This magnetic field is N H I. 3.2 l When a conducting coil is placed in a magnetic field, the magnetic flux is..h.a 3.3 Where 0 is the magnetic permeability of free space and is the magnetic permeability of the environment (the air environment in this experiment). If the magnetic field H does not change, the magnetic flux remains constant. The magnetic field and the magnetic flux passing through the bobbin cross-sectional area is induced a voltage and current. The magnitude and direction of the induced voltage and current depends on how the magnetic field changes. This is known as the Faraday Law. Now see the Faraday's influence in a bobbin and any other bobbin that comes close to it. Faraday Law
dt If we use equation 3.3, 9 U d N 3.4 dh U.A.N 3.5 dt Here, N, number of turns of the current carrying coil (bobbin). When another coil with the number of winding of N 2 is brought close, a voltage U is induced in this bobbin is given as di N 2 U 0 N 3.6 dt l After giving this brief information, now let's define the expressions related with our experiment. In our experiment, we will bring a coil closer to another one which is a currentcarrying coil. According to Faraday's law, there is an induction current in this second bobbin and accordingly a magnetic field. Induced voltage in second bobbin is given as where L is 2 2 N U ind. N. N. 0..A..I L.I 3.7 l N.r L 0 3.8 l and it is called coil induction constant (Inductance). The conditions (l>>r) may not be met in practice. In this case, the following expression, which yields more accurate results than the formula 3.8, can be used. So, for l>r, it is advisable to use the following formula: 3/4 L=2. 0 3.9.In the experiment, the inductance of each coil will be determined by using different coils. The resonance frequency for LC circuits is given f = 0 2 3.0 The inductance can be easily determined here: 2
2 L= 2 0 3. Experimental Procedure Figure 3.. Experiment setup ) Set up the test setup as shown. Here, there are two separate circuits and the induction current is generated according to the Faraday law in the second circuit by changing the magnetic field generated in the first circuit. The first circuit consists of the wave source and the bobbin, the second circuit consists of the coil, the capacitor and the oscilloscope. 2) Apply the low frequency sin wave voltage to the first circuit and change the frequency until the resonance frequency is observed from the oscilloscope. (Note: The sinusoidal wave appearing at the resonance frequency oscillation has the maximum amplitude.) 3) Provide the resonance condition for each coil, read the period values from the oscilloscope, and calculate the resonance frequency from the equation f 0 T 0. No N 2r/mm l/mm Cat. No. T(s) fresonans (s-) L 300 40 60 006.0 2 300 32 60 006.02 3 300 26 60 006.03 4 200 40 05 006.04 5 00 40 53 006.05 6 50 26 60 006.06
7 75 26 60 006.07 4) Take note of the capacitance value of the capacitors used in the system. Ctop=... 5) Calculate the inductance of each material separately using the formula with the values found. 6) Using these values, draw the plots; fres i. N 2 vs. L for 3, 6, 7 coil ii. /l vs. L/N 2 for, 4, 5 coil iii. L vs. r 2 for, 2, 3 coil 2 2 N r. These graphs are expected to be linear according to L 0... equation. Find l the slopes of these lines. 7) For each of the three cases, obtain 0.. A. Are the results for three values A A A, 2, 3 close to each other? If not, why? 8) Create a conclusion and comments on the experiment. 9) Answer the questions in the booklet. Example Plot for (6.i. ):
Questions : ) What do Ampere and Faraday laws reveal? 2) What is the frequency and period of a wave and how is it measured by means of oscilloscope? 3) What is the resonance? Drive the equation for resonance frequency of a RLC circuits. 4) What does the inductance of a coil depend on? 5) Calculate the induction electromotive force generated between the ends of the coil as the magnetic flux passing through a 00-turns coil drops from 30 maxwell to 0 maxwell in 0.5 seconds 6) Describe the difference between magnetic field B and magnetic flux in your own words. Are these magnitudes vector or scalar? What are the units? How are these units related to each other?