Chapter 19 Magnetism Conceptual questions: 5,6,8,14,16 Quick Quizzes: 1,2,5 Problems: 2,19,24,30,34,40,46

Magnets Poles of a magnet are the ends where objects are most strongly attracted Two poles, called north and south Like poles repel each other and unlike poles attract each other If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole There are no magnetic charges or monopoles

Magnetic Field Lines, Unlike Poles Iron filings are used to show the pattern of the electric field lines The direction of the field is the direction a north pole would point Compare to the electric field produced by an electric dipole

Magnetic Field Lines, Like Poles Iron filings are used to show the pattern of the electric field lines The direction of the field is the direction a north pole would point Compare to the electric field produced by like charges

Magnetic and Electric Fields An electric field surrounds any stationary electric charge A magnetic field surrounds any moving electric charge A magnetic field surrounds any magnetic material

Earth’s Magnetic Field The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core

Magnetic Fields When moving through a magnetic field, a charged particle experiences a magnetic force whose magnitude is given by F=q v B sinq where B – magnetic field q – charge v – its speed q - the angle between the direction of V and the direction of B

Units of Magnetic Field The SI unit of magnetic field B is the Tesla (T) Wb is a Weber The cgs unit is a Gauss (G) 1 T = 104 G

Finding the Direction of Magnetic Force Experiments show that the direction of the magnetic force is always perpendicular to both v and B Fmax occurs when v is perpendicular to B F = 0 when v is parallel to B

Right Hand Rule Point your fingers in the direction of v Curl your fingers in the direction of B The direction of the force on a positive charge is directed along the thumb If the charge is negative, the force is opposite that determined by the right hand rule

QUICK QUIZ 19.1 A charged particle moves in a straight line through a certain region of space. The magnetic field in that region (a) has a magnitude of zero, (b) has a zero component perpendicular to the particle's velocity, or (c) has a zero component parallel to the particle's velocity.

QUICK QUIZ 19.2 The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?

Conceptual questions 5. How can the motion of a charged particle be used to distinguish between a magnetic and electric fields in a certain region? 6. Which way would a compass point if you were at the north magnetic pole of the Earth?

Problem 19.2 Find the direction of the force on a proton moving through the magnetic fields shown in Fig. 19.2. Repeat for the electron.

Conceptual Question 14

Magnetic Force on a Current Carrying Conductor A force is exerted on a current-carrying wire placed in a magnetic field F = B I l sinq l – length of the conductor I – current in the conductor The direction of the force is given by right hand rule

Force on a Wire

Problem 19.19 An unusual message delivery system is pictured in Figure P19.19. A 15-cm length of conductor that is free to move is held in place between two thin conductors. When a 5.0-A current is directed as shown in the figure, the wire segment moves upward at a constant velocity. If the mass of the wire is 15 g, find the magnitude and direction of the minimum magnetic field that is required to move the wire.

Torque on a Current Loop N is the number of turns in the coil t = N B I A sinq

Electric Motor An electric motor converts electrical energy to mechanical energy An electric motor consists of a current-carrying loop that rotates when placed in a magnetic field

Problem 19.24. A rectangular loop consists of 100 closely wrapped turns and has dimensions 0.40 m by 0.30 m. The loop is hinged along the y axis, and the plane of the coil makes an angle of 30.0° with the x axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field of 0.80 T directed along the x axis, when the current in the windings has a value of 1.2 A in the direction shown? What is the expected direction of rotation of the loop?

MCAD question

Force on a Charged Particle in a Magnetic Field The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle Solving for r:

Quiz 19.3 As a charged particle moves freely in a circular path in the presence of a constant magnetic field applied perpendicular to the particle's velocity, its kinetic energy (a) remains constant, (b) increases, (c) decreases.

MCAD question

Problem 19.30. Consider the mass spectrometer shown schematically below. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m = 2.18 × 10–26 kg.

Magnetic Fields – Long Straight Wire A current-carrying wire produces a magnetic field The compass needle points in the direction of the magnetic field produced by the current The magnitude of the field at a distance r from a wire carrying a current of I is µo = 4  x 10-7 T m / A µo is called the permeability of free space

Direction of the Field of a Long Straight Wire Right Hand Rule #2 Grasp the wire in your right hand Point your thumb in the direction of the current Your fingers will curl in the direction of the field

Problem 19-34 What is the direction of the current in the wire in figures a, b, and c?

Problem 19. 40. The two wires in figure below carry currents of 3 Problem 19.40. The two wires in figure below carry currents of 3.00 A and 5.00 A in the direction indicated. (a) Find the direction and magnitude of the magnetic field at a point midway between the wires. (b) Find the magnitude and direction of the magnetic field at point P, located 20.0 cm above the wire carrying the 5.00-A current.

Magnetic Force Between Two Parallel Conductors The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2 The force per unit length is:

QUICK QUIZ 19.5 If I1 = 2 A and I2 = 6 A in the figure below, which of the following is true: (a) F1 = 3F2, (b) F1 = F2, or (c) F1 = F2/3?

Problem 19.46. In Figure, the current in the long, straight wire is I1 = 5.00 A, and the wire lies in the plane of the rectangular loop, which carries 10.0 A. The dimensions are c = 0.100 m, a = 0.150 m, and L = 0.450 m. Find the magnitude and direction of the net force exerted by the magnetic field due to the straight wire on the loop.

Magnetic Field of a Current Loop All the segments, Δx, contribute to the field, increasing its strength Magnetic field at the center of the ring is B=m I/2R

Magnetic Field of a Current Loop – Total Field

Magnetic Field of a Solenoid If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid It is also known as an electromagnet since it acts like a magnet only when it carries a current

Magnetic Field in a Solenoid, Magnitude The magnitude of the field inside a solenoid is constant at all points far from its ends B = µo n I n is the number of turns per unit length n = N / ℓ

Magnetic Effects of Electrons - Orbits An individual atom should act like a magnet because of the motion of the electrons about the nucleus Each electron circles the atom once in about every 10-16 seconds This would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular path However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom The net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials

Magnetic Effects of Electrons -- Spins Electrons also have spin The classical model is to consider the electrons to spin like tops In some materials, the spins do not naturally cancel Such materials are called ferromagnetic

Magnetic Effects of Electrons -- Domains In some materials, the spins do not naturally cancel Such materials are called ferromagnetic Large groups of atoms in which the spins are aligned are called domains When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become magnetized

Domains Large groups of atoms in which the spins are aligned are called domains When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become magnetized Random alignment, a, shows an unmagnetized material When an external field is applied, the domains aligned with B grow, b

Conceptual questions: 8. A magnet attracts a piece of iron. The iron can then attract another piece of iron. On the basis of domain alignment explain what happens in each piece of iron. 12. Why does hitting a magnet with a hammer cause the magnetism to be reduced? 16. How can a current loop be used to determine the presence of a magnetic field in a given region of space? 17. A hanging Slinky toy is attached to a powerful battery and a switch. When the switch is closed so that the current flows through the Slinky, does the Slinky compress or expand?

Magnetic levitation train (maglev) Japanese MLX01 can travel at speeds over 500 km/h (310 mi/h)

Review questions 1.What is the force on a 1 C charge moving at 1 m/s perpendicular to a magnetic field with a strength of 1 tesla? A. 0 N B. 1 N C. 2 N D. 3 N 2. The SI unit for the magnetic field strength is a: A. wortle B. newton C. tesla D. volt-meter

3. All of the following are true EXCEPT: a. breaking a magnet in half will create two magnets each with equal and opposite poles b. the magnetic north pole is near the geographic south pole c. like poles and charges repel, opposite attract d. a stationary charge close to a magnetic needle can move that needle.

True or False. Consider a force on a charge moving through a constant magnetic field. The direction of the force depends on the angle between the velocity and the magnetic field. The force is always perpendicular to both the velocity and the magnetic field. The force is always parallel to both the velocity and the magnetic field. The force is maximum when the velocity is in the same direction as the magnetic field.

MCAT A beam of electrons is traveling to the right. What is the direction of the magnetic field at point A? A. into the page  B. out of the page C. to the right D. to the left A

MCAT, cont. 1. A current I is flowing clockwise through a wire loop. Point P is in the middle of the loop. What is the direction of the magnetic field at point P? out of the page b. to the right c. into the page d. to the left 2. In the above example, a proton is at point P and moving upward, in the plane of the page. What is the direction of the acceleration of the proton? to the left b. to the right up, that is speeding up the proton down, that is slowing down the proton