Lecture 17 Sources of the Magnetic Field

1. Lecture 17Sources of the Magnetic Field General Physics II, Lec 17, By/ T.A. Eleyan

2. History • 1819 Hans Christian Oersted discovered that a compass needle was deflected by a current carrying wire • Then in 1920s Jean-Baptiste Biot and Felix Savart performed experiments to determine the force exerted on a compass by a current carrying wire General Physics II, Lec 17, By/ T.A. Eleyan

3. Biot & Savart’s Results • dB the magnetic field produced by a small section of wire • ds a vector the length of the small section of wire in the direction of the current • r the positional vector from the section of wire to where the magnetic field is measured • I the current in the wire • angle between ds & r General Physics II, Lec 17, By/ T.A. Eleyan

4. dB perpendicular to ds • |dB| inversely proportional to |r|2 • |dB| proportional to current I • |dB| proportional to |ds| • |dB| proportional to sin q General Physics II, Lec 17, By/ T.A. Eleyan

5. Biot–Savart Law All these results could be summarised by one “Law” Putting in the constant Where m0 is the permeablity of free space General Physics II, Lec 17, By/ T.A. Eleyan

6. Magnetic Field due to Currents The passage of a steady current in a wire produces a magnetic field around the wire. • Field form concentric lines around the wire • Direction of the field given by the right hand rule. If the wire is grasped in the right hand with the thumb in the direction of the current, the fingers will curl in the direction of the field. • Magnitude of the field General Physics II, Lec 17, By/ T.A. Eleyan

7. [Q]: The two wires in the figure below carry currents of 3.00A and 5.00A in the direction indicated. Find the direction and magnitude of the magnetic field at a point midway between the wires. 5.00 A 3.00 A 20.0 cm General Physics II, Lec 17, By/ T.A. Eleyan

8. Magnetic Field of a current loop Dx1 Magnetic field produced by a wire can be enhanced by having the wire in a loop. 1 loop Current I B I N loops Current  NI Dx2 General Physics II, Lec 17, By/ T.A. Eleyan

9. [Q] What is the magnetic field at point Q in Fig.? [Q] What is the magnitude and direction of the magnetic field at point P in Fig.? General Physics II, Lec 17, By/ T.A. Eleyan

10. [Q] Use the Biot-Savart Law to calculate the magnetic field B at C, the common center of the semicircular area AD and HJ of radii R1=8 cm and R2=4 cm, forming part of the circuit ADJHA carrying current I=10 A, as seen figure. General Physics II, Lec 17, By/ T.A. Eleyan

11. Ampere’s Law Consider a circular path surrounding a current, divided in segments ds, Ampere showed that the sum of the products of the field by the length of the segment is equal to mo times the current. General Physics II, Lec 17, By/ T.A. Eleyan

12. Example By way of illustration, let us use Ampere's law to find the magnetic field at a distance r from a long straight wire, a problem we have solved already using the Biot-Savart law General Physics II, Lec 17, By/ T.A. Eleyan

13. Magnetic Force between two parallel conductors General Physics II, Lec 17, By/ T.A. Eleyan

14. Force per unit length General Physics II, Lec 17, By/ T.A. Eleyan

15. Definition of the SI unit Ampere Used to define the SI unit of current called Ampere. If two long, parallel wires 1 m apart carry the same current, and the magnetic force per unit length on each wire is 2x10-7 N/m, then the current is defined to be 1 A. General Physics II, Lec 17, By/ T.A. Eleyan

16. Example Two wires, each having a weight per units length of 1.0x10-4 N/m, are strung parallel to one another above the surface of the Earth, one directly above the other. The wires are aligned north-south. When their distance of separation is 0.10 mm what must be the current in each in order for the lower wire to levitate the upper wire. (Assume the two wires carry the same current). l 1 I1 2 d I2 General Physics II, Lec 17, By/ T.A. Eleyan

17. F1 1 I1 B2 mg/l 2 d I2 l General Physics II, Lec 17, By/ T.A. Eleyan

18. Magnetic Field of a solenoid • Solenoid magnet consists of a wire coil with multiple loops. • It is often called an electromagnet. General Physics II, Lec 17, By/ T.A. Eleyan

19. Solenoid Magnet • Field lines inside a solenoid magnet are parallel, uniformly spaced and close together. • The field inside is uniform and strong. • The field outside is non uniform and much weaker. • One end of the solenoid acts as a north pole, the other as a south pole. • For a long and tightly looped solenoid, the field inside has a value: General Physics II, Lec 17, By/ T.A. Eleyan

20. Since the field lines are straight inside the solenoid, the best choice for amperian loop is a rectangle: abcd. Winding density: n=N/L where N = total number of windings and L = total length. Integrate: General Physics II, Lec 17, By/ T.A. Eleyan

21. Solenoid Magnet The field inside has a value: n = N/L : number of (loop) turns per unit length. I : current in the solenoid. General Physics II, Lec 17, By/ T.A. Eleyan

22. Example: Consider a solenoid consisting of 100 turns of wire and length of 10.0 cm. Find the magnetic field inside when it carries a current of 0.500 A. General Physics II, Lec 17, By/ T.A. Eleyan

23. General Physics II, Lec 17, By/ T.A. Eleyan