Learning Objectives

Learning Objectives

Learning Objectives
(See related pages)

Concepts and Skills to Review

sketching and interpreting electric field lines (Section 16.4)
uniform circular motion; radial acceleration (Section 5.2)
torque; lever arm (Section 8.2)
relation between current and drift velocity (Section 18.3)

Mastering the Concepts

Magnetic field lines are interpreted just like electric field lines. The magnetic field at any point is tangent to the field line; the magnitude of the field is proportional to the number of lines per unit area perpendicular to the lines.
Magnetic field lines are always closed loops because there are no magnetic monopoles.
The smallest unit of magnetism is the magnetic dipole. Field lines emerge from the north pole and reenter at the south pole. A magnet can have more than two poles, but it must have at least one north pole and at least one south pole.
The magnitude of the cross product of two vectors is the magnitude of one vector times the perpendicular component of the other:
The direction of the cross product is the direction perpendicular to both vectors that is chosen using right hand rule 1.
The magnetic force on a charged particle is
If the charge is at rest (u = 0) or if its velocity has no component perpendicular to the magnetic field _{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663827/V_B.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>} then the magnetic force is zero. The force is always perpendicular to the magnetic field and to the velocity of the particle.

Direction: use the right-hand rule to find _{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/299142/ch19_vcrossB.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>} then reverse it if q is negative.
The SI unit of magnetic field is the tesla:
If a charged particle moves at right angles to a uniform magnetic field, then its trajectory is a circle. If the velocity has a component parallel to the field as well as a component perpendicular to the field, then its trajectory is a helix.
The magnetic force on a straight wire carrying current I is

where_{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663827/L.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>}is a vector whose magnitude is the length of the wire and whose direction is along the wire in the direction of the current.
The magnetic torque on a planar current loop is

where q is the angle between the magnetic field and the dipole moment vector of the loop. The direction of the dipole moment is perpendicular to the loop as chosen using right-hand rule 1 (take the cross product of_{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663827/L.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>}for any side with_{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663827/L.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>}for the next side, going around in the same direction as the current).
The magnetic field at a distance r from a long straight wire has magnitude

The field lines are circles around the wire with the direction given by right-hand rule 2.
The permeability of free space is
The magnetic field inside a long tightly wound solenoid is uniform:

Its direction is along the axis of the solenoid, as given by right-hand rule 3.
Ampere's law relates the circulation of the magnetic field around a closed path to the net current I that crosses the interior of the path.
The magnetic properties of ferromagnetic materials are due to an interaction that keeps the magnetic dipoles aligned within regions called domains, even in the absence of an external magnetic field.

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Home > Chapter 19 > Learning Objectives

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	Course-wide Content
		MCAT Practice Test MCAT Review Inside Cover Content f...

	Quizzes
		Multiple Choice Quiz Interactive Quiz: Magn...
	More Resources
		Learning Objectives
	Animated Examples
		Interactive: Magnetic ... Cornell Interactives