# Chapter 21. Magnetic Forces and Magnetic Fields

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1 Chapter 21 Magnetic Forces and Magnetic Fields

2 21.1 Magnetic Fields The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.

3 21.1 Magnetic Fields The behavior of magnetic poles is similar to that of like and unlike electric charges.

4 21.1 Magnetic Fields Surrounding a magnet there is a magnetic field. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point.

5 21.1 Magnetic Fields The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet.

6 21.1 Magnetic Fields

7 21.2 The Force That a Magnetic Field Exerts on a Charge When a charge is placed in an electric field, it experiences a force, according to F =q E

8 21.2 The Force That a Magnetic Field Exerts on a Charge The following conditions must be met for a charge to experience a magnetic force when placed in a magnetic field: 4. The charge must be moving. 5. The velocity of the charge must have a component that is perpendicular to the direction of the magnetic field.

9 21.2 The Force That a Magnetic Field Exerts on a Charge Right Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field 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 charge. If the moving charge is negative, the direction of the force is opposite to that predicted by RHR-1.

10 21.2 The Force That a Magnetic Field Exerts on a Charge DEFINITION OF THE MAGNETIC FIELD The magnitude of the magnetic field at any point in space is defined as F B= q o vsin θ where the angle (0< <180 o ) is the angle between the velocity of the charge and the direction of the magnetic field. SI Unit of Magnetic Field: newton second coulomb meter =1 tesla T 1 gauss=10 4 tesla

11 21.2 The Force That a Magnetic Field Exerts on a Charge Example 1 Magnetic Forces on Charged Particles A proton in a particle accelerator has a speed of 5.0x10 6 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes and angle of 30.0 degrees with respect to the proton s velocity (see part (c) of the figure). Find (a) the magnitude and direction of the force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration of the particle were an electron?

12 21.2 The Force That a Magnetic Field Exerts on a Charge (a) F = q o vb sin θ= C m/ s 0. 40T sin N (b) a= F m p = N kg = m/s 2 (c) Magnitude is the same, but direction is opposite. a= F m e = N kg = m/ s 2

13 21.3 The Motion of a Charged Particle in a Magnetic Field Charged particle in an electric field. Charged particle in a magnetic field.

14 21.3 The Motion of a Charged Particle in a Magnetic Field Conceptual Example 2 A Velocity Selector A velocity selector is a device for measuring the velocity of a charged particle. The device operates by applying electric and magnetic forces to the particle in such a way that these forces balance. How should an electric field be applied so that the force it applies to the particle can balance the magnetic force?

15 21.3 The Motion of a Charged Particle in a Magnetic Field The electrical force can do work on a charged particle. The magnetic force cannot do work on a charged particle.

16 21.3 The Motion of a Charged Particle in a Magnetic Field The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. F c =m v 2 r qvb=m v2 r r= mv qb

17 21.3 The Motion of a Charged Particle in a Magnetic Field Conceptual Example 4 Particle Tracks in a Bubble Chamber The figure shows the bubble-chamber tracks from an event that begins at point E. At this point a gamma ray travels in from the left, spontaneously transforms into two charged particles. The particles move away from point A, producing two spiral tracks. A third charged particle is knocked out of a hydrogen atom and moves forward, producing the long track. The magnetic field is directed out of the paper. Determine the sign of each particle and which particle is moving most rapidly.

18 21.4 The Mass Spectrometer r= mv qb = mv eb 1 2 mv 2 =ev magnitude of electron charge KE=PE m= er 2 2V B2

19 21.4 The Mass Spectrometer The mass spectrum of naturally occurring neon, showing three isotopes.

20 21.5 The Force on a Current in a Magnetic Field The magnetic force on the moving charges pushes the wire to the right.

21 21.5 The Force on a Current in a Magnetic Field F =qvb sin θ F = Δq t Δ I v Δ t L B sin θ F =ILB sin θ

22 21.5 The Force on a Current in a Magnetic Field Example 5 The Force and Acceleration in a Loudspeaker The voice coil of a speaker has a diameter of m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and the cone. (b) The voice coil and cone have a combined mass of kg. Find their acceleration.

23 21.5 The Force on a Current in a Magnetic Field (a) F =ILB sin θ = 2.0 A [55 π m ] T sin N (b) a= F m = 0.86 N 2 =43 m/s kg

24 21.5 The Force on a Current in a Magnetic Field

25 21.6 The Torque on a Current-Carrying Coil The two forces on the loop have equal magnitude but an application of RHR-1 shows that they are opposite in direction.

26 21.6 The Torque on a Current-Carrying Coil The loop tends to rotate such that its normal becomes aligned with the magnetic field.

27 21.6 The Torque on a Current-Carrying Coil Net torque=τ =ILB 1 2 φ w sin ILB φ 1 w sin =IAB sin φ 2 magnetic moment τ =NIA overbracealignl B sin φ number of turns of wire

28 21.6 The Torque on a Current-Carrying Coil Example 6 The Torque Exerted on a Current-Carrying Coil A coil of wire has an area of 2.0x10-4 m 2, consists of 100 loops or turns, and contains a current of A. The coil is placed in a uniform magnetic field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil. (f) Find the maximum torque that the magnetic field can exert on the coil. (a) magnetic moment NIA overbracealignl = A m 2 = A m 2 (b) τ =NIA overbracealignl magnetic moment B sin φ= A m T sin 90 = N m

29 21.6 The Torque on a Current-Carrying Coil The basic components of a dc motor.

30 21.6 The Torque on a Current-Carrying Coil

31 21.7 Magnetic Fields Produced by Currents Right-Hand Rule No. 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, and the tips of the fingers will point in the direction of the magnetic field.

32 21.7 Magnetic Fields Produced by Currents A LONG, STRAIGHT WIRE B= μ o I 2πr μ o =4π 10 7 T m/ A permeability of free space

33 21.7 Magnetic Fields Produced by Currents Example 7 A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x10-6 C and is moving parallel to the wire at a distance of m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.

34 21.7 Magnetic Fields Produced by Currents F =qvb sin θ=qv μ o I 2πr sin θ B= μ o I 2πr

35 21.7 Magnetic Fields Produced by Currents Current carrying wires can exert forces on each other.

36 21.7 Magnetic Fields Produced by Currents Conceptual Example 9 The Net Force That a Current-Carrying Wire Exerts on a Current Carrying Coil Is the coil attracted to, or repelled by the wire?

37 21.7 Magnetic Fields Produced by Currents A LOOP OF WIRE B= μ o I 2R center of circular loop

38 21.7 Magnetic Fields Produced by Currents Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of m. Find the magnitude and direction of the magnetic field at the center of the loop.

39 21.7 Magnetic Fields Produced by Currents B= μ o I 1 2πr μ o I 2 2R = μ o I 1 2 πr I 2 R B= 4π 10 7 T m/ A A π m 2. 0 A m = T

40 21.7 Magnetic Fields Produced by Currents The field lines around the bar magnet resemble those around the loop.

41 21.7 Magnetic Fields Produced by Currents

42 21.7 Magnetic Fields Produced by Currents A SOLENOID Interior of a solenoid B=μ o ni number of turns per unit length

43 21.7 Magnetic Fields Produced by Currents A cathode ray tube.

44 21.8 Ampere s Law AMPERE S LAW FOR STATIC MAGNETIC FIELDS For any current geometry that produces a magnetic field that does not change in time, B Δ =μ o I net current passing through surface bounded by path

45 21.8 Ampere s Law Example 11 An Infinitely Long, Straight, Current-Carrying Wire Use Ampere s law to obtain the magnetic field. B Δ =μ o I B Δ = μ o I B2π r= μ o I B= μ o I 2πr

46 21.9 Magnetic Materials The intrinsic spin and orbital motion of electrons gives rise to the magnetic properties of materials. In ferromagnetic materials groups of neighboring atoms, forming magnetic domains, the spins of electrons are naturally aligned with each other.

47 21.9 Magnetic Materials

48 21.9 Magnetic Materials

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