1. Chapter 21 Magnetic Forces and Magnetic Fields

2. 21.1 Magnetic Fields • Magnets, as you know, can exert forces on one another. • In electricity, we talk about negative and positive dipoles or charges. • In magnetism, we discuss north and south poles. • Like poles repel each other, and unlike poles attract.

3. Electric charges vs. Magnets Electric charges Magnets Have a negative end and a positive end. ALL MAGNETS have a negative and positive or north and south end. Produce a magnetic field that is a vector quantity Magnetic field direction is determined by the direction of the north pole of a compass at a particular point Lines tend to originate at north and end at south without stopping in between • Can be positive or negative • Positive and negative charges can be separated so that a (+) or (-) charge is isolated. • Produce an electric field that is a vector quantity • Electric field points away from positive and toward negative

4. Some Vocabulary • Angle of declination: angle that a compass needle deviates from the north geographic pole • Angle of dip: the angle that the magnetic field makes with respect to the surface at any point • Magnetic north pole: true north pole as generated by the earth due, most likely, to currents of iron moving in the core • Geographic north pole: where the Earth’s axis of rotation crosses the surface in the Northern Hemisphere • Click here for an interactive description of the difference.

5. 21.2 The Force that a Magnetic Field Exerts on a Moving Charge • Magnetic force can be added to our bucket list of forces that can cause objects to accelerate and can be used in conjunction with Newton’s 2nd Law of Motion. • For a Charge to Experience a magnetic force when place in a field: • The charge must be moving, for no magnetic force acts on a stationary charge. • The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field.

6. Force on Moving Charge • If the charge moves parallel or antiparallel to the field, the charge experiences no magentic force. • If the charge moves perpendicular to the field, the charge experience the maximum possible magnetic force. • If the charge moves at an angle,θ, only the velocity component (vsinθ), perpendicular to the field gives rise to a magnetic force.

7. Right-Hand Rule #1 • Extend the right hand so the fingers point along the direction of the magnetic field (B) and the thumb points along the velocity of the charge. The palm of the hand, then, faces in the direction of the magnetic force that acts on a positive test charge. • If the moving charge is negative, the direction of the magnetic force is opposite from described above.

8. Definition of Magnetic Field • Direction of field is determined by a small compass needle. • SI Unit: Newton second/coulomb meter = 1 Tesla • If magnetic field is much less than one Tesla, a gauss (G) is often used as a unit for magnetic field. • 1 gauss = 10-4tesla

9. 21.3 Motion of a Charged Particle Electric Field Magnetic Field Direction of magnetic force is always perpendicular to magnetic field and velocity Since displacement and force are perpendicular, no work is done by this force Force changes direction but not magnitude of velocity • Direction of electric force is same as direction of electric field • Force does work and increases KE

10. The Circular Trajectory • When a +q charge is moving perpendicular to a magnetic field, the magnetic force causes the particle to move in a circular path. • Radius of the circle is inversely proportional to the magnitude of the magnetic field • Stronger fields produce “tighter” circular paths

11. The Force on a Current in a Magnetic Field • Since an electric current is a collection of moving charges, a current in the presence of a magnetic field can also experience a magnetic force • Modify RHR-1 by replacing direction of velocity with direction of conventional current in order to determine direction of force. • The magnetic force is maximum when the wire is oriented perpendicular to the magnetic field.

12. Magnetic Force on current-carrying wire • Simplified, this equation becomes • The direction of the force of the magnetic field is determined by using RHR-1 as explained on previous slide. • If the direction of the current changes, the direction of the force will also change.

13. The Torque on a Current-Carrying Coil • If a loop of wire is suspended properly in a magnetic field, the magnetic force produces a torque that can rotate the loop. • This torque is responsible for the operation of an electric motor. • When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned with the magnetic field. • Basically, the current loop behaves like a magnet suspended in a magnetic field.

14. Physics of DC Electric Motor • http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c1 • http://www.learnapphysics.com/apphysicsb/magnetism.php

15. Magnetic Fields Produced by Currents • A current-carrying wire will produce a magnetic field of its own. • A compass needle will align itself with the net magnetic field produced by a current and the magnetic field of the earth • Thus, the beginning of the study of electromagnetism.

16. Long, Straight Wires • Compass needles indicate that the magnetic field lines produced by the current are circles centered on the wire. • If the current reverses, the needles reverse. • Direction of field found by RHR-2 • RHR-2: curl the fingers of the right hand into the shape of a half circle. Point the thumb in the direction of the conventional current, I and the tips of the fingers will point in the direction of the magnetic field

17. Long, Straight Wires • Magnitude of B is directly proportional to I and inversely proportional to the radial distance from the wire • is known as the permeability of free space with a value of 4πx 10-7 Tm/A