III.Sources of Magnetic Fields - Ampere s Law - solenoids

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1 Magnetism I. Magnetic Field - units, poles - effect on charge II. Magnetic Force on Current - parallel currents, motors III.Sources of Magnetic Fields - Ampere s Law - solenoids IV.Magnetic Induction - Faraday s Law - Lenz s Law

2 The student will be able to: Define and illustrate the basic properties of magnetic fields and permanent magnets: field lines, north and south poles, magnetic compasses, Earth s magnetic field. Solve problems relating magnetic force to the motion of a charged particle through a magnetic field, such as that found in a mass spectrometer. Solve problems involving forces on a current carrying wire in a magnetic field and torque on a current carrying loop of wire in a magnetic The student field. will be able to: and apply relation between magnetic field and position for a long current State carrying and apply wire and relation solve related between problems. magnetic field and position for a long Qualitatively describe and apply properties of magnetic dipole fields generated by loops of current and model behavior of magnetic materials current using carrying domains, ferromagnetism, wire and solve paramagnetism, related and diamagnetism. problems. State and apply Faraday s Law and Lenz s Law and solve problems involving induced emf and magnetic flux. HW: HW:

3 I B The magnetic field around a long straight current consists of concentric circles, seen here at an oblique angle. The direction of the field is given by a right hand rule: thumb in direction of current, fingers curl and point in direction of the field.

4 B I Same field seen from above such that the long straight current is out of the page directly toward the eye.

5 A view of a plane that contains the long straight current I B field points into the page ( ) on one side of the current and out of the page ( ) on the other side.

6 Magnetic Field of infinite Linear Current B I r B = m 0I 2pr B = magnetic field strength I = current (source of B) r = perpendicular distance from I μ 0 = permeability constant

7 I B μ 0 = 4π 10 7 N/A 2 r B = m 0I 2pr The constant μ 0 in this equation is known as the magnetic permeability of free space applies to a vacuum or essentially the same for air.

8 I B r B = m 0I 2pr

9 Magnetic Field Antiparallel Currents The field shown here is the net field of two currents Credit: Geek3, Wikipedia

10 Magnetic Field Antiparallel Currents B net B 1 B 2 I 1 I 2 Magnetic fields follow the superposition principle! Credit: Geek3, Wikipedia

11 Draw a vector diagram illustrating superposition at each of four locations, with appropriate relative lengths of the arrows: I I

12 B net

13 Magnetic Field Parallel Currents B net Credit: Geek3, Wikipedia

14 Ampere s Law Simplified Version Ampere s Law describes the magnetic field in the vicinity of any current (not just an infinite straight one). B = magnetic field (average or constant) I = current (source of B) l = length of path that goes around I

15 Ampere s Law Simplified Version In certain special cases this law may be used to solve for an unknown magnetic field. However, it is necessary to analyze a path surrounding a certain current along which the field is either constant and parallel to the path, perpendicular to the path, and/or nonexistent. B = magnetic field (average or constant) I = current (source of B) l = length of path that goes around I

16 Ampere s Law Example l B r I B = m 0I 2pr For a long, straight current in a wire, a circular path of radius r will be parallel to the field and the field will have constant magnitude along this path. By Ampere s Law the product of the field and the circumference of the circle must equal μ 0 I.

17 Magnetic Field Antiparallel Currents r I 1 I 2 B avg = m 0I 1 2pr In this example the product of the average field strength and the circumference of the circle must equal μ 0 I 1 the presence of I 2 makes the field nonuniform along the path. Credit: Geek3, Wikipedia

18 Magnetic Field Ring of Current I N S Credit: Geek3, Wikipedia

19 Magnetic Field Ring of Current S I N A ring of current produces a magnetic dipole acts like a bar magnet. Credit: Geek3, Wikipedia

20 Magnetic Field Solenoid S N Credit: Geek3, Wikipedia

21 Magnetic Field Solenoid Credit: Geek3, Wikipedia

22 Magnetic Field Ideal Infinite Solenoid I B B 0nI or B 0NI L B = field anywhere inside (uniform) n = number of turns per length N = number of turns (or coils) of wire L = length of cylinder I = current

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