Chapter 27 Magnetism

27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-2: Measuring a magnetic field. A rectangular loop of wire hangs vertically as shown. A magnetic field B is directed horizontally, perpendicular to the wire, and points out of the page at all points. The magnetic field is very nearly uniform along the horizontal portion of wire ab (length l = 10.0 cm) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward magnetic force (in addition to the gravitational force) of F = 3.48 x N when the wire carries a current I = A. What is the magnitude of the magnetic field B?

The force on a moving charge is related to the force on a current: Once again, the direction is given by a right-hand rule Force on an Electric Charge Moving in a Magnetic Field

Magnetic Force on a point charge Force on a moving charge Direction: Right hand rule F is Perpendicular to both and Lay hand along palm toward q  Thumb points along q  Thumb points opposite = out of page Arrow coming at you = into page Arrow leaving you

Magnetic Force on a point charge Direction: RIGHT Hand Rule Perpendicular to both v and B Here Into or Out of the page Run fingers along v, curl them towards B, If q is positive, thumb points along F If q is negative, thumb points opposite F Direction: RIGHT Hand Rule Perpendicular to both v and B Here Into or Out of the page Run fingers along v, curl them towards B, If q is positive, thumb points along F If q is negative, thumb points opposite F

Magnetic Force on a point charge If q is + find the direction of F B v B v B v F F F

Problem (I) Determine the direction of for each case in Fig. 27–43, where represents the maximum magnetic force on a positively charged particle moving with velocity

27-4 Force on an Electric Charge Moving in a Magnetic Field Example 27-5: Magnetic force on a proton. A magnetic field exerts a force of 8.0 x N toward the west on a proton moving vertically upward at a speed of 5.0 x 10 6 m/s. When moving horizontally in a northerly direction, the force on the proton is zero. Determine the magnitude and direction of the magnetic field in this region. (The charge on a proton is q = +e = 1.6 x C.)

If a charged particle is moving (electron) perpendicular to a uniform magnetic field, its path will be a circle. What if you have a proton? 27-4 Force on an Electric Charge Moving in a Magnetic Field

Example 27-7: Electron’s path in a uniform magnetic field. An electron travels at 2.0 x 10 7 m/s in a plane perpendicular to a uniform T magnetic field. Describe its path quantitatively.

Problem solving: Magnetic fields – things to remember: 1.The magnetic force is perpendicular to the magnetic field direction. 2.The right-hand rule is useful for determining directions. The right-hand rule gives the direction. 3.Equations in this chapter give magnitudes only Force on an Electric Charge Moving in a Magnetic Field

Aurora Borealis: Northern Lights Aurora Australis: Southern Lights Due to ions (e - & p + ) from the Sun – Travel from Sun to Earth in ~ 3 days 93 million miles in 3 days ~ 30 million miles/day Aurora on 11/20/03, Zagreb, Croatia. Photo by Hrvoje Horvat Charged particles in B-fields

Ions steered to poles by Earth’s mag. field – Collide with molecules in atmosphere ionize particles, recombination produces light: Aurora – More energetic particles get closer to Earth Aurora

Lorentz Equation

Mass Spectrometer For selected speeds

v B B Electromagnetic Flowmeter E ∆V F E = F B qE = qvB We know B since we applied it. E is determined from  V and the width of the artery d E=  V/d d + - Charges build until forces balance!

27-4 Force on an Electric Charge Moving in a Magnetic Field Conceptual Example 27-10: Velocity selector, or filter: crossed E and B fields. Some electronic devices and experiments need a beam of charged particles all moving at nearly the same velocity. This can be achieved using both a uniform electric field and a uniform magnetic field, arranged so they are at right angles to each other. Particles of charge q pass through slit S 1 and enter the region where B points into the page and E points down from the positive plate toward the negative plate. If the particles enter with different velocities, show how this device “selects” a particular velocity, and determine what this velocity is.