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Chapter 22

Magnetism (Lecture II)

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Outline Motion of charged particles in a

magnetic field Magnetic force on a current-

carrying wire Electric current and magnetic fields Magnitude of the magnetic field of

a current-carrying wire Solenoids

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The Motion of Charged Particles in a Magnetic Field

The electromagnetic flowmeter

The operating principle of a mass spectrometer

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The Magnetic Force on a Current-Carrying Wire

Magnitude of the magnetic force on a current-carrying wire F = ILBsin I: Current in the wire (A); L:

Length of the wire (m); B: Magnetic field (T); : The angle between the direction of the magnetic field and the current.

Direction of the magnetic force on a current-carrying wire Given by the same Magnetic

Force RHR for charges

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Example 22-4: Magnetic Levity

A copper rod 0.150 m long and with a mass of 0.0500 kg is suspended from two thin, flexible wires. At right angles to the rod is a uniform magnetic field of 0.550 T pointing into the page. Find the direction and

magnitude of the electric current needed to levitate the copper rod.

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Electric Current and Magnetic Fields

The source of any magnetic field is the motion of electric charge.

Magnetic field produced by a straight and infinitely long current-carrying wire:

The magnetic field “circulates” around the wire.

Find the direction of the magnetic field using the magnetic field RHR.

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Conceptual Checkpoint 22-5

The magnetic field shown in the sketch is due to the horizontal, current-carrying wire. Does the current in

the wire flow to the left or to the right?

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Magnitude of the Magnetic Field of a Current-Carrying Wire

Magnitude of the magnetic field, B, produced by a straight and infinitely long current-carrying wire: B = (0I)/(2r) 0 = 4 x 10-7 Tm/A, the

permeability of free space. The field doubles if the

current I is doubled; the field halves if the distance from the wire, r, is doubled.

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Example 22-6: An Attractive Wire

A 52-C charged particle moves parallel to a long wire with a speed of 720 m/s. The separation between the particle and the wire is 13 cm, and the magnitude of the force exerted on the particle is 1.4 x 10-7 N. Find the magnitude of the

magnetic field, B. Find the current in the wire,

I.

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Solenoids A solenoid carrying a current

produces an intense, nearly uniform magnetic field inside the loops.

A solenoid is also called an electromagnet.

The magnetic field inside the solenoid is directed along its axis. The field outside the solenoid is almost zero.

Magnitude of the magnetic field inside a solenoid:

B = 0 (N/L) I = 0 nI n: the number of loops per unit

length

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Example 22-7: Through the Core of a Solenoid

A solenoid is 20.0 cm long, has 200 loops, and carries a current of 3.25 A. Find the magnitude of the

force exerted on a 15.0-C changed particle moving at 1050 m/s through the interior of the solenoid, at an angle of 11.5° relative to the solenoid’s axis.

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Homework #7

Chapter 22, P. 793-795, Problems: #31, 33, 49, 57 (Physics, Walker, 4th edition).