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Lecture 17 Sources of the Magnetic Field

Lecture 17 Sources of the Magnetic Field. 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.

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Lecture 17 Sources of the Magnetic Field

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  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

  24. Lecture 18 Discussion General Physics II, Lec 17, By/ T.A. Eleyan

  25. [1] What is the net force on the rectangular loop of wire in Fig. ? The force on the top and bottom of the loop are equal and opposite so they cancel. General Physics II, Lec 17, By/ T.A. Eleyan

  26. [2] What is the net force per unit length on the wire carrying 2A in Fig. ? The 2A wire is attracted to the 1A wire (force up) and attracted to the 3A wire ( force down). Thus, the force per unit length on the 2A wire is General Physics II, Lec 17, By/ T.A. Eleyan

  27. [3] What is the magnitude and direction of the magnetic field at point P in Fig. ? General Physics II, Lec 17, By/ T.A. Eleyan

  28. [4] What is the magnitude and direction of the magnetic field at point Q in Fig.? General Physics II, Lec 17, By/ T.A. Eleyan

  29. [5] An electron moves is a circular orbit with diameter 10 cm in a 5 Tesla magnetic field. What is the time it takes the electron to complete one orbit? General Physics II, Lec 17, By/ T.A. Eleyan

  30. [6] A proton moves with a velocity of v = (2iˆ- 4jˆ +kˆ ) m/s in a region in which the magnetic field is B " (iˆ + 2jˆ - 3kˆ ) T. What is the magnitude of the magnetic force this charge experiences? General Physics II, Lec 17, By/ T.A. Eleyan

  31. [7] A conductor suspended by two flexible wires as shown in Figure has a mass per unit length of 0.040 0 kg/m. What current must exist in the conductor in order for the tension in the supporting wires to be zero when the magnetic field is 3.60 T into the page? What is the required direction for the current? General Physics II, Lec 17, By/ T.A. Eleyan

  32. [8] A positive charge q = 3.20 × 10-19 C moves with a velocity v = (2iˆ + 3jˆ - kˆ ) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving charge (in unit-vector notation), taking B = (2iˆ + 4jˆ + kˆ ) T and E =(4iˆ - jˆ - 2kˆ ) V/m. (b) What angle does the force vector make with the positive x axis? General Physics II, Lec 17, By/ T.A. Eleyan

  33. [9] A nonconducting sphere has mass 80.0 g and radius 20.0 cm. A flat compact coil of wire with 5 turns is wrapped tightly around it, with each turn concentric with the sphere. As shown in Figure, the sphere is placed on an inclined plane that slopes downward to the left, making an angle θ with the horizontal, so that the coil is parallel to the inclined plane. A uniform magnetic field of 0.350 T vertically upward exists in the region of the sphere. What current in the coil will enable the sphere to rest in equilibrium on the inclined plane? Show that the result does not depend on the value of !. General Physics II, Lec 17, By/ T.A. Eleyan

  34. [10] The segment of wire in Figure carries a current of I =5.00 A, where the radius of the circular arc is R = 3.00 cm. Determine the magnitude and direction of the magnetic field at the origin. General Physics II, Lec 17, By/ T.A. Eleyan

  35. [11]Figure shows a section of a long hallow cylindrical of radii a=5cm and b=10 cm, carrying a uniform distributed current I, the magnitude of the magnetic field on its outer surface at r=b is measured to be B=0.2T, where r is the radial distance from the cylindrical axis. (a) Find the current in the wire? General Physics II, Lec 17, By/ T.A. Eleyan

  36. (b) Find the magnitude of the magnetic field at r=20 cm? General Physics II, Lec 17, By/ T.A. Eleyan

  37. (c) Find the magnitude of the magnetic field at r=8 cm? General Physics II, Lec 17, By/ T.A. Eleyan

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