Chapter 19 Magnetism

19.1 Magnets

<Permanent Magnets>

• North magnetic pole (N) and South magnetic pole (S)

• Like poles repel each other, and unlike poles attract.

• Magnetic Field Electric Field

• Magnetic poles cannot be isolated (the important difference between electric charges and magnetic poles).

• The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. (Figure 19.1)

• The magnetic field at any point is tangent to the magnetic field line at that point. The strength of the magnetic field is proportional to the number of lines per unit area that passes through a surface oriented perpendicular to the lines. (Similar to the electric field lines)

19.2 Magnetic Field of The Earth (Reading Assignment)

<Geomagnetism>

• The geographic north pole corresponds to a magnetic south pole, and the geographic south pole corresponds to a magnetic north pole.

19.3 Magnetic Fields

• A stationary charged particle does not interact with a static magnetic field.

<The Nature of the Magnetic Force>

• A charge placed in a magnetic field experiences a magnetic force.

1. The charge must be moving, for no magnetic force acts on a stationary charge.

2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field.

• Right-Hand Rule No.1, RHR-1, (Figure 19-6)

Fingers: (magnetic field)

Thumb: (velocity of the charge)

Palm: (magnetic force)

• The magnetic force on a charged particle moving in a magnetic field is

F = q v B sin (19.1)

Where q is the magnitude of the charge, v is the velocity of the charge, B is the strength of the external magnetic field, and is the angle between and .

• The magnetic field can be defined as the magnetic force exerted on a positive test charge at that point.

<Definition of the Magnetic Field>

� Definition of the Magnetic Field �

The magnitude B of the magnetic field at any point in space is defined as

B = (19.2)

Where F is the magnitude of the magnetic force on a positive test charge q and v is the velocity of the charge and makes an angle (0 180°) with the direction of the magnetic field. The magnetic field is a vector, and its direction can be determined by using a small compass needle.

SI unit of magnetic field: 1 T (tesla) = 1 = 1

1 T = 10⁴ G(gauss)

• Examples

19.4 Magnetic Force on a Current-Carrying Conductor

• A charge moving through a magnetic field experiences a magnetic force. A current-carrying wire placed in a magnetic field can also experience a magnetic force.

• The direction of the magnetic force is given by RHR-1.

• Figure 19.8

• Magnetic force on a current carrying wire of length

F = BI sin (19.6)

where I is the current in the wire, the length of the wire, B the magnetic field, and the angle between and the direction of the current.

• Examples

19.5 Torque on a Current Loop

<The Torque>

• The magnetic force produces a torque (, Tau) that rotates the current-carrying loop. (ex. Electric motors)

• Figure 19.13

• When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned with the magnetic field.

• The net torque on the loop is

= NBIA sin

where A is the area of the loop, B the magnetic field, I the current, and the angle between the normal to the plane of the loop and the direction of the magnetic field.

• Examples

19.6 The Galvanometer and Its Applications (Reading Assignment)

19.7 Motion of a Charged Particle in a Magnetic Field

<The Circular Trajectory>

• Figure 19.18

• The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path.

• Find the radius of the path in Figure 19.18

r = (19.10)

• Examples

<The Work Done on a Charged Particle Moving Through Electric and Magnetic Fields>

• The magnetic force always acts in a direction that is perpendicular to the motion of the charge. Consequently, the displacement of the moving charge never has a component in the direction of the magnetic force. The magnetic force cannot do work and change kinetic energy of the charged particle.

<Comparing Particle Motion in Electric and Magnetic Field>

21.7 Magnetic Fields of a Long, Straight Wire and Ampere’s Law

• A current-carrying wire produces a magnetic field. (Figure 19.22) (electromagnetism)

<A Long, Straight Wire>

• Right-Hand Rule No.2, RHR-2, (Figure 19-23)

Fingers: (magnetic field)

Thumb: (current)

• The magnitude of the magnetic field in a long, straight wire is

B = (19.11)

where I is the current and r is the radial distance from the wire.

The constant µ_o (Mu-zero) is known as the permeability of free space, and its value is µ_o = 4x 10^-7 T-m/A

• Examples

<Ampere’s Law and a Long, Straight Wire>

19.9 Magnetic Force Between Two Parallel Conductors

• Figure 19.26

• The magnetic field set up by Wire 2, which carries current I₂, at Wire 1 is

B₂ =

• The magnetic force on Wire 1 in the presence of field B₂ due to I₂ is

F₁ = B₂I₁ =

• The magnetic force per unit length on Wire 1

=

• Examples

19.10 Magnetic Field of A Current Loop

• Figure 19.27

• The magnetic field at the center of a loop is

B =

Where I the current and R the radius of the loop.

• Figure 19.28

19.11 Magnetic Field of A Solenoid

• A solenoid is a long coil of wire in the shape of a helix (Figure 19.29).

• The magnitude of the magnetic field in the interior of a long solenoid is

B = µ_o n I (21.7)

Where n is the number of turns per unit length of the solenoid (n = N / ) and I is the current.

• The field inside the solenoid and away from its ends is nearly constant in magnitude and directed parallel to the axis.

• Electromagnets are usually made of a solenoid.

• Examples

19.12 Magnetic Domains (Reading Assignment)