# Lecture 7 Magnetic Field and Magnetic Force Chapter

• Slides: 12

Lecture 7 Magnetic Field and Magnetic Force Chapter 19. 1 19. 6 Outline • • Magnets Magnetic Field Magnetic Force Motion in a Magnetic Field

Magnets The simplest magnet is a somehow magnetized bar of iron. It attracts and holds other pieces of iron. Most of the force a magnet exerts from its ends. A magnet’s ends point north and south. The north-pointing end is called the north pole. The south-pointing end is called the south pole. Like magnet poles repel one another, unlike poles attract one another.

Magnetic Poles Positive and negative charges in neutral matter can be separated from each other. The north and south magnetic poles cannot be separated. Every time we saw a magnet in half, it gets the 2 poles. Magnetic properties have all substances, but to a different extent. Iron is one of the best magnets.

Magnetic Field The presence of a magnet alters properties of space near it. The altered space is called a force field. We cannot see a force field, but can detect its presence by its effects. The form of the magnetic field can be traced by a pattern of iron filings. They line up in the direction in which a piece of iron would move if put there (field lines). They gather most thickly where the force on the iron would be the greatest (larger field line density).

Origin of the Magnetic Field Every electric current has a magnetic field around it. This was first shown by Oersted in 1820. The current and the field are perpendicular to each other. The direction of the magnetic field can be found by encircling the wire with the fingers of the right hand. The direction of the current along the wire is then shown by the thumb. All magnetic fields originate from moving electric charges.

The Electromagnetic Field An electric charge at rest is surrounded by only an electric field. When it is moving, a magnetic field around it appears. The relative motion between the charge and observer is needed to produce a magnetic field. Both an electric and magnetic field are aspects of a single electromagnetic field that surrounds every electric charge.

Magnetic Field A charged object, moving through a magnetic field, experiences a magnetic force. The force has a maximum strength when the charge moves perpendicularly to the magnetic filed lines. The magnetic force is experimentally defined as: q is the magnitude of a test charge v is the charge velocity F = q v B sin B is the strength of the external magnetic filed is the angle between the directions of v and B

Units of Magnetic Field The SI unit of magnetic fields is tesla (T) F = q v B sin N N T = = Cm/s Am F B = q v sin If v || B F = 0 If v B F = q v B

Magnetic Field Problem: A proton moves perpendicularly to a uniform magnetic field B at 107 m/s and experiences an acceleration of 2 1013 m/s 2 in the +x direction when its velocity is in +z direction. Find the magnitude and direction of the field. F B = q v sin F=ma Direction of B is y m = 1. 67 10 27 kg F = 3. 34 10 14 N q = 1. 6 10 19 C sin = 1 B = 0. 02 T

Magnetic Force on a Current. Carrying Conductor Current is a collection of moving charges the resultant force on the wire (conductor) is the sum of the individual forces on the charged particles. Let us calculate a force acting on a piece of wire of length l and cross-sectional area A in a uniform external magnetic field B, perpendicular to the wire. vd drift velocity of the charge Fmax = (q vd B) (n A l) n total number of charges per volume I = n q vd A Fmax = B I l F = B I l sin

Motion of a Charged Particle in a Magnetic Field The magnetic force is always toward the center of the circular path the magnetic force causes a centripetal acceleration, changing the direction of v. mv 2 F = q v B = r mv r = q. B The radius of the path is proportional to the momentum of and is inversely proportional to the magnetic field.

Summary • Gravity, electric, and magnetic forces alter properties of the surrounding space. These properties are called force fields. • Electromagnetic forces is one of the 4 fundamental forces which exist in the Universe. • A single electromagnetic field surrounds every moving electric charge.