Chapter 29: Magnetic Fields 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!! Chapter 29 Outline Magnets & Magnetic Fields  B Fields Electric Currents Produce B Fields!! Force on an Electric Current in a B Field; Definition of B Force on an Electric Charge moving in a B Field Torque on a Current Loop Magnetic Dipole Moment  μ Applications: 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 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 two points Diametrically opposed to each other. He called the points poles

James Clerk Maxwell 1600: William Gilbert 1750: 1819: 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 1820’s: Faraday and Henry 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.

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 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. 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 In other words, magnetic poles are 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. In other words, 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 Reminder: An electric field surrounds any electric charge. Similarly, The region of space surrounding any moving electric charge also contains a magnetic field. 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. Magnetic field lines 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

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. 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) 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 loop hangs from a balance which measures a downward magnetic force (in addition to gravity) 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). Straight portions each have length l within the field. Calculate the net force F on the wire due to B0. 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.

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). Straight portions each have length l within the field. 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.