PHYS 1444 – Section 003 Lecture #15AnnouncementsMagnetic FieldEarth’s Magnetic FieldElectric Current and MagnetismDirections in a Circular Wire?Magnetic Forces on Electric CurrentSlide 8Slide 9About the Magnetic Field, BExample 27 – 1Example 27 – 2Magnetic Forces on a Moving ChargeSlide 14Example 27 – 3Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu1PHYS 1444 – Section 003Lecture #15Monday, Oct. 24, 2005Dr. Jaehoon Yu•Magnetic field•Earth’s magnetic field•Magnetic field by electric current•Magnetic force on electric current•Magnetic force on a moving chargeToday’s homework is homework #8, due noon, next Tuesday!!Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu2Announcements•Reading assignments–CH. 27 – 6–CH. 27 – 8–CH. 27 – 9Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu3–The direction of the magnetic field is tangent to a line at any point–The direction of the field is the direction the north pole of a compass would point to–The number of lines per unit area is proportional to the strength of the magnetic field–Magnetic field lines continue inside the magnet–Since magnets always have both the poles, magnetic field lines form closed loops unlike electric field lines Magnetic Field•Just like the electric field that surrounds electric charge, a magnetic field surrounds a magnet•What does this mean?–Magnetic force is also a field force–The force one magnet exerts onto another can be viewed as the interaction between the magnet and the magnetic field produced by the other magnet–What kind of quantity is the magnetic field? Vector or Scalar?•So one can draw magnetic field lines, too.VectorMonday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu4 Earth’s Magnetic Field•Now what magnetic pole does the geographic north pole has to have?–Magnetic south pole. What? How do you know that?–Since the magnetic north pole points to the geographic north, the geographic north must have magnetic south pole•The pole in the north is still called geomagnetic north pole just because it is in the north–Similarly, south pole has north magnetic pole•The Earth’s magnetic poles do not coincide with the geographic poles magnetic declination–Magnetic north pole is in northern Canada, some 1300km off the true north pole•Earth’s magnetic field line is not tangent to the earth’s surface at all points–The angle the Earth’s field makes to the horizontal line is called the angle dipMonday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu5 Electric Current and Magnetism•In 1820, Oersted found that when a compass needle is placed near an electric wire, the needle deflects as soon as the wire is connected to a battery and a current flows–Electric current produces a magnetic field•The first indication that electricity and magnetism are the same thing–What about a stationary electric charge and magnet?•They don’t affect each other.•The magnetic field lines produced by a current in a straight wire is in the form of circles following the “right-hand” rule–The field lines follow right-hand’s fingers wrapped around the wire when the thumb points to the direction of the electric currentMonday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu6 Directions in a Circular Wire?•OK, then what are the directions of the magnetic fields generated by the current flowing through circular loops?Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu7 Magnetic Forces on Electric Current•Since the electric current exerts force on a magnet, the magnet should also exert force on the electric current–Which law justifies this?•Newton’s 3rd law–This also was found by Oersted•Direction of the force is always –perpendicular to the direction of the current and also–perpendicular to the direction of the magnetic field, B•Experimentally the direction of the force is given by another right-hand rule When the fingers of the right-hand points to the direction of the current and the finger tips bent to the direction of magnetic field B, the direction of thumb points to the direction of the forceMonday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu8 Magnetic Forces on Electric Current•OK, we are set for the direction but what about the magnitude?•It is found that the magnitude of the force is directly proportional to–the current in the wire–The length of the wire in the magnetic field (if the field is uniform)–The strength of the magnetic field•The force also depends on the angle between the directions of the current and the magnetic field–When the wire is perpendicular to the field, the force is strongest–When the wire is parallel to the field, there is no force at all•Thus the force on current I in the wire w/ length l in a uniform field B issinF IlB q�Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu9 Magnetic Forces on Electric Current•Magnetic field strength B can be defined using the previous proportionality relationship w/ the constant 1:•if =90o, and if =0o•So the magnitude of the magnetic field B can be defined as– where Fmax is the magnitude of the force on a straight length l of wire carrying a current I when the wire is perpendicular to B•The relationship between F, B and I can be written in vector formula: –l is the vector whose magnitude is the length of the wire and its direction is along the wire in the direction of the conventional current–This formula works if B is uniform.•If B is not uniform or l does not make the same angle everywhere, the infinitesimal force acting on a differential length dl is sinF IlB q=maxF IlB=min0F =maxB F Il=F Il B= �rr rdF Idl B= �rr rMonday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu10 About the Magnetic Field, B•It is a vector quantity•The SI unit for B is tesla (T)–What is the definition of 1 Tesla in terms of other known units?–1T=1N/Am–In older names tesla is weber per meter-squared•1Wb/m2=1T•The cgs unit for B is gauss (G)–How many T is one G?•1G=10-4 T–For computation, one MUST convert G to T at all times•Magnetic field on the Earth’s surface is about 0.5G=0.5x10-4T•On a diagram, for field coming out and for going in. e�Monday, Oct. 24, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu11Example 27 – 1 Measuring a magnetic field. A rectangular loop of wire hangs
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