Experiment No: EM 4 Experiment Name: Biot-Savart Law Objectives: Measuring the magnetic field of a current passing through long straight and conductor wire as a function of the current. Measuring the magnetic field at the center and at distances away from the center of a current loop. Measuring the magnetic field of at the center and at distances away from the center of a solenoid Theoretical Background: According to Biot- B at a point P for a conductor traversed by the current (I) is made up of the contributions of the infinitesimal parts of conductor, the length and direction of which are described by the vector dl. Let's consider the current distribution in figure 6.1. Figure 6.1. The contribution of current element dl to the magnetic field at a point P is db. Since Idl and are in figure plane, db is perpendicular and out of the page. A current element makes a contribution db to the magnetic field at point P. The position vector from the infinitesimal current element to P is given as the Biot-Savart law. 6.1 The direction of db is given by the direction of vector multiplication and is out of the page. In this case, the contributions of the infinitesimal parts of conductor is given by: 6. where is angle between dl and.
Calculating the total magnetic field thus means evaluating an integral. Analytic solutions can be given only for conductors with certain symmetries. The magnetic field of an infinitely long wire is 6.3 at distance R from the axis (see Fig. 6. ). The magnetic field made by a current in a straight wire curls around the wire in a ring. You can find it by pointing your right thumb in the direction of the current in the wire and curling your fingers. Your fingers will be curled in the same direction as the magnetic field around the wire. Figure 6.. Magnetic field of an infinitely long wire. The magnetic field of circular conductor loop carrying current I with the radius a is at a distance x on the axis through the centre of the loop. Its field lines are paralel to the axis (see Fig. 6.3). 6.4 Figure 6.3. Magnetic field of a circular conductor loop.
Setup and the Experiment A) The Experimental Setup for a Straight Conductor To find the magnetic field at the center and at the different points away from the center of a linear line current, set up the experimental apparatus as shown in Figure 6.4. Figure 6.4. Exprimental setup for measuring the magnetic field at a straight conductor In this setup, we will first investigate the dependence of magnetic field at the center of the wire to the current passing through the wire. To do this, move the probe tip closer to the center of the wire (1mm) and fix it there Connect the tangential B-probe to gaussmeter, and calibrate the gaussmeter (for calibration; plug in B-probe to calibration hole and pull down set button and read the minimum magnetic field. Adjust the power supply at 4 volt. Increase the current I from 0 to 16 A. Each time measure the magnetic field values from the gaussmeter. Then write to Table 6.1. Draw a graph the magnetic field of the straight conductor as a function of the current I. Table 6.1 I (A) 0 4 6 8 10 1 14 16 18 0
In the same setup, fixed the power supply at 4 volt and current value 10 A. Move the Bprobe from the centre of straight conductor to the written x values in Table 6.. Each time the measure the magnetic field value and write to Table 6.. Draw a graph the magnetic field B of the straight conductor as a function of the distance x from the axis of the conductor. Table 6. x (cm) 0.0 0.5 1.0 1.5.0.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 B) The Experimental Setup for a Circular Conductor Loop To find the magnetic field at the center and at the different points away from the center of a circular loop, set up the experimental apparatus as shown in Figure 6.5. Figure 6.5 Experimental setup for measuring the magnetic field at circular conductor loops Replace the holder for the straight conductor with the adapter for conductor loops (b) and attach the conductor loop (R=60mm, 40mm, 0mm respectively). Align the B-probe towards the centre of the conductor loop.
For each the conductor loop, adjust the power supply at 4 volt. Increase the current I from 0 to 16 A. Each time measure the magnetic field values from the gaussmeter. Then write to Table 6.3. Draw a graph the magnetic field of the conductor loop as a function of current I. Table 6.3 I (A) 0 4 6 8 10 1 14 16 R=0 mm R=40 mm R=60 mm In the same setup, fixed the power supply at 4 volt and current value 16 A. Move the Bprobe from the centre of conductor loop to the written x values in Table 6.4. Each time measure the magnetic field value and write to Table 6.4. Draw a graph the magnetic field of the conductor loop as a function of the distance x from the axis of the conductor. Table 6.4 X (cm) 1 3 5 6 7 8 9 10 R=0 mm R=40 mm R=60 mm C) The experimental Setup For a Solenoid To find the magnetic field at the center and at the different points away from the center of a solenoid, set up the experimental apparatus as before and attach the solenoid with radius R 45 mm. Fixed the power supply at 4 volt and current value 10 A. Move the B-probe from the centre of conductor loop to written x values in Table 6.5. Each time the measure the magnetic field value and write to Table 6.5. Draw a graph the change of magnetic field of the solenoid with the distance of x from axis of the solenoid.
Table 6.5 x (cm) 0 1 3 5 7 10 15 Attach the solenoid that can be changed number of turns for the change of the magnetic field of the centre of the solenoid with number of turns in unit distance Measure the magnetic field of the centre of the solenoid by changing the number of turns in cm under V=4 V, I=10 A constant values. Draw a graph the change of magnetic field of the solenoid with the number of turns. Questions: 1-) What does Biot Savart law physically mean? Explain. -) What does Ampere's law physically mean? Explain. 3