Ch. 20: Magnetic Fields & Forces Chapter 27 opener. Magnets produce magnetic fields, but so do electric currents. An electric current flowing in this straight wire produces a magnetic field which causes the tiny pieces of iron (iron “filings”) to align in the field. We shall see in this Chapter how magnetic field is defined, and that the magnetic field direction is along the iron filings. The magnetic field lines due to the electric current in this long wire are in the shape of circles around the wire. We also discuss how magnetic fields exert forces on electric currents and on charged particles, as well as useful applications of the interaction between magnetic fields and electric currents and moving electric charges.

Electric Currents Produce B Fields!! Magnetism Outline Magnets & Magnetic Fields  B Fields Electric Currents Produce B Fields!! Force on Electric Current in a B Field; Definition of B Force on a moving Electric Charge in a B Field Torque on a Current Loop Magnetic Dipole Moment  μ

Applications: Outline Motors, Loudspeakers, Galvanometers Discovery & Properties of the Electron The Hall Effect Mass Spectrometer

Brief History of Magnetism 13th Century BC: The Chinese used a compass. Uses a magnetic needle Probably an invention of Arabic or Indian origin 800 BC: The Greeks Discovered that magnetite (Fe3O4) attracts pieces of iron

He called the points poles History 1269: Pierre de Maricourt Found that the direction of a needle near a spherical natural magnet formed lines that encircled the sphere. The lines also passed through 2 points diametrically opposed to each other. He called the points poles

1750: Experimenters showed that magnetic poles exert attractive or 1600: William Gilbert Expanded experiments with magnetism to a variety of Materials Suggested the Earth itself was a large permanent magnet 1750: Experimenters showed that magnetic poles exert attractive or repulsive forces on each other. 1819: Found that an electric current deflected a compass needle

James Clerk Maxwell: 1819: Found that an electric current deflected a compass needle 1820’s: Faraday and Henry Found further connections between electricity and magnetism A changing magnetic field creates an electric field. James Clerk Maxwell: A changing electric field produces a magnetic field.

Hans Christian Oersted 1777 – 1851: Discovered a relationship between electricity & magnetism. He found that an electric current in a wire will deflect a compass needle. He was the first to find evidence of a connection between electric & magnetic phenomena. Also was the first to prepare pure Aluminum.

Experiments show that: Magnetic fields are produced Magnetism Physics is an Experimental Science! Experiments show that: Magnetic fields are produced by moving electric charges Magnetic fields exert forces on other moving charges

The Focus of this chapter: Magnetism The Focus of this chapter: Understand the sources of magnetic fields & the fields they produce Calculate the magnetic force on a charged particle Magnetism & electricity are connected More connections will be studied in later chapters

Magnets Permanent magnet applications: The first observations of magnetic fields involved permanent magnets Many ancient cultures discovered natural magnetic properties of materials: Magnetite & Others Permanent magnet applications: Compass needles Speakers Computer hard disks

Bar Magnet A bar magnet is a permanent magnet in the shape of a bar. The symbol for the magnetic field is B. The magnetic field lines can be found from the pattern of the iron filings The filings are small, needle-shaped, permanent magnets

Magnets & Magnetic Fields Every magnet, regardless of its shape, has two ends called “Poles”. They are the “North (N) Pole” & the “South (S) Pole” The poles exert forces on one another: Like poles repel & opposite poles attract Figure 27-2. Like poles of a magnet repel; unlike poles attract. Red arrows indicate force direction.

The North pole of a magnet The poles received their names due to the way a magnet behaves in the Earth’s magnetic field: If a bar magnet is suspended so that it can move freely, it will rotate. The North pole of a magnet points toward the Earth’s North magnetic pole.

Earth’s North magnetic pole is actually a magnetic South pole! This means that Earth’s North magnetic pole is actually a magnetic South pole! Similarly, the Earth’s South magnetic Pole is actually a magnetic North pole!

A single magnetic pole has never been isolated. The force between two poles varies as the inverse square of the distance between them. (Similar to the force between 2 point charges) A single magnetic pole has never been isolated. That is, magnetic poles are always found in pairs. All attempts so far to detect an isolated magnetic pole (a magnetic monopole) have been unsuccessful. No matter how many times a permanent magnet is cut in 2, each piece always has north & south poles.

If a magnet is cut in half, the result isn’t a north pole & a south pole!! The result is two smaller magnets!! Figure 27-3. If you split a magnet, you won’t get isolated north and south poles; instead, two new magnets are produced, each with a north and a south pole.

Magnetic Fields: Observations Reminder: An electric field surrounds any electric charge. Similarly, The region of space surrounding any moving electric charge also contains a magnetic field.

Magnetic Fields: Observations A magnetic field also surrounds a magnetic substance making up a permanent magnet. A magnetic field is a vector quantity. It is symbolized by B. The direction of field B is given by the direction the North pole of a compass needle points in that location. Iron filings can be used to show how the field lines, as traced out by a compass, would look.

Magnetic Field Lines, which are always closed loops. Magnetic fields can be visualized using Magnetic Field Lines, which are always closed loops. Figure 27-4. (a) Visualizing magnetic field lines around a bar magnet, using iron filings and compass needles. The red end of the bar magnet is its north pole. The N pole of a nearby compass needle points away from the north pole of the magnet. (b) Magnetic field lines for a bar magnet.

Magnetic Field Lines, Bar Magnet A compass can be used to trace the field lines. The lines outside the magnet point from the North pole to the South pole. Iron filings can also be used to show the pattern of the magnetic field lines. The direction of the magnetic field is the direction a north pole would point.

Magnetic Field Lines Opposite Poles Like Poles

Magnetic Field Lines The magnetic poles are indicated at the ends of the bar magnet Called north and south The magnetic poles are analogous to positive and negative charges The north poles of the filings are attracted to the south pole of the bar magnet

Plotting Field Lines Field lines are three-dimensional A large dot (•) indicates the tip of the vector when it points out of the plane A cross (×) denotes the tails of the vector when it points into the plane

The SI unit of magnetic field B Magnetic Fields The iron filings align parallel to the magnetic field lines The SI unit of magnetic field B is the Tesla (T) The magnetic field lines go from the north pole toward the south pole The magnitude of the field decreases as you move farther from a pole The magnetic field lines form closed loops General property of magnetic fields, not just bar magnets

Horseshoe Magnet The field is largest in the horseshoe gap Can be made by bending a bar magnet There are poles at the ends of the horseshoe The field is largest in the horseshoe gap The field is directed across the gap

Earth’s Magnetic Field Earth’s magnetic field is very small: BEarth  50 μT It depends on location & altitude. It is also slowly changing with time! Note!!! The Earth’s magnetic “North Pole” is really a South Magnetic Pole, because the North poles of magnets are attracted to it. Figure 27-5. The Earth acts like a huge magnet; but its magnetic poles are not at the geographic poles, which are on the Earth’s rotation axis.

Earth’s Magnetic Field The source of the Earth’s magnetic field is likely convection currents in the Earth’s core. There is strong evidence that the magnitude of a planet’s magnetic field is related to its rate of rotation. The direction of the Earth’s magnetic field reverses Periodically (over thousands of years!).

A Uniform Magnetic Field is constant in magnitude & direction. The magnetic field B between these two wide poles is nearly uniform. Figure 27-7. Magnetic field between two wide poles of a magnet is nearly uniform, except near the edges.

Electric Currents Produce Magnetic Fields Experiments show that Electric Currents Produce Magnetic Fields. The direction of the field is given by a Right-Hand Rule. Figure 27-8. (a) Deflection of compass needles near a current-carrying wire, showing the presence and direction of the magnetic field. (b) Magnetic field lines around an electric current in a straight wire. (c) Right-hand rule for remembering the direction of the magnetic field: when the thumb points in the direction of the conventional current, the fingers wrapped around the wire point in the direction of the magnetic field. See also the Chapter-Opening photo.

Right-Hand Rule. Magnetic Field Due to a Current Loop The direction is given by a Right-Hand Rule. Figure 27-9. Magnetic field lines due to a circular loop of wire. Figure 27-10. Right-hand rule for determining the direction of the magnetic field relative to the current.

Force on a Current in a Magnetic Field & the DEFINITION of B A magnet exerts a force F on a current-carrying wire. The direction of F is given by a Right-Hand Rule Figure 27-11. (a) Force on a current-carrying wire placed in a magnetic field B; (b) same, but current reversed; (c) right-hand rule for setup in (b).

This equation defines the Magnetic Field B. The force F on the wire depends on the current, the length l of the wire, the magnetic field B & its orientation: This equation defines the Magnetic Field B. In vector notation the force is given by The SI Unit of the Magnetic Field B is The Tesla (T): 1 T  1 N/A·m Another unit that is sometimes used (from the cgs system) is The Gauss (G): 1 G = 10-4 T

Example: Magnetic Force on a Current Carrying Wire A wire carrying a current I = 30 A has length l = 12 cm between the pole faces of a magnet at angle θ = 60° as shown. The magnetic field is approximately uniform & is B = 0.90 T. Calculate the magnitude of the force F on the wire. Solution: F = IlBsin θ = 2.8 N.

Example: Magnetic Force on a Current Carrying Wire A wire carrying a current I = 30 A has length l = 12 cm between the pole faces of a magnet at angle θ = 60° as shown. The magnetic field is approximately uniform & is B = 0.90 T. Calculate the magnitude of the force F on the wire. Solution: F = IlBsin θ = 2.8 N. Solution: Use Solve & get: F = 2.8 N

Example: Measuring a Magnetic Field A rectangular wire loop hangs vertically. A magnetic field B is directed horizontally, perpendicular to the wire, & points out of the page. B is uniform along the horizontal portion of wire (l = 10.0 cm) which is near the center of the gap of the magnet producing B. Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.

Example: Measuring a Magnetic Field The top portion of the loop is free of the field. The loop hangs from a balance which Measures a downward magnetic force (in addition to gravity) of F = 3.48  10-2 N when the wire carries a current I = 0.245 A. Calculate B. Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.

Example: Measuring a Magnetic Field The downward magnetic force (in addition to gravity) is F = 3.48  10-2 N when the wire carries a current I = 0.245 A. Calculate B. Solution: Use Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T. Solve & get: B = 1.42 T

Example: Magnetic Force on a Semicircular Wire. A rigid wire carrying a current I consists of a semicircle of radius R & two straight portions. It lies in a plane perpendicular to a uniform magnetic field B0. (Note the choice of x & y axes). Solution: The forces on the straight sections are equal and opposite, and cancel. The force dF on a segment dl of the wire is IB0R dφ and is perpendicular to the plane of the diagram. Therefore, F = ∫dF = IB0R∫sin φ dφ = 2IB0R. The straight portions have length l within the field. Calculate the net force F on the wire due to B0.

Example: Magnetic Force on a Semicircular Wire. Calculate the net force F on the wire due to B0. Solution gives: F = 2IB0R Solution: The forces on the straight sections are equal and opposite, and cancel. The force dF on a segment dl of the wire is IB0R dφ and is perpendicular to the plane of the diagram. Therefore, F = ∫dF = IB0R∫sin φ dφ = 2IB0R.