General Physics II Magnetic Fields and Forces 1
Magnetism Magnetism underlies the operation of the hard disk drive, which is the mainstay of modern electronic information storage, from computers to ipods. Magnetism is intimately related to electricity. We shall see later that moving charges (a current) produce magnetic effects. Most common magnetic effects are observed in the vicinity of permanent magnets. Every permanent magnet (or simply, magnet ) has two regions where the magnetic effects are most intense. These are called the poles. 2
Magnetism 3
Magnetism If a magnet broken into two pieces, two magnets will result. There are no isolated magnetic poles. This is unlike electric charge, since positive and negative charges can be separated. A compass is a magnet that can rotate freely in response to magnetic forces. 4
Magnetism Either pole of a magnet will attract certain magnetic materials such as iron, which are not initially magnets themselves. Like electrostatically induced charges, which are due to electric polarization, magnetic materials also become polarized magnetically when in the vicinity of a magnetic pole. The material acquires induced magnetic poles and the magnetic polarization leads to the attraction. Note that only a few elements are magnetic at room temperature: iron, cobalt, and nickel. How Magnets Work 5
Magnetic Field Every moving charge and permanent magnet produces a magnetic field in the space around it. If the N pole of another magnet is brought into this field, the pole will experience a force in the direction of the field at the location of the pole. A magnet placed in a magnetic field will experience a torque tending to align the axis of the magnet with the direction of the magnetic field at its location. Thus, small magnets, e.g., compasses, can be used to map the direction of a magnetic field at different points in space. Magnetic field lines are drawn such that the direction of the field at a given location is tangent to the field line at that point. The magnetic field is a vector quantity. 6
Magnetic Field 7
The Earth is a Magnet 8
Two identical bar magnets are placed at right angles as shown. In what direction will the N pole of the compass needle point at the location shown? 1.Straight up 2.Straight down 3.At a 45º angle, upward and to the right 4.At a 45º angle, upward and to the left 5.None of the above 9
Workbook: Chapter 24, Questions 1 and 2 10
Magnetic Field of a Straight Current- Carrying Wire As mentioned before, moving charges produce magnetic fields in all space. A steady current in a long, straight wire produces circular magnetic field lines with the wire at the center. 11
Magnetic Field of a Straight Current- Carrying Wire B Current out of page 12
Workbook: Chapter 24, Questions, 6,7,10 13
Magnetic Field of a Current Loop Reverse the direction of the current and the field lines reverse direction. Magnetic field lines always form closed curves. 14
Magnetic Field of a Solenoid A solenoid is a coil, usually having many closely-spaced loops. The field is stronger inside solenoid than outside. Also, the field is nearly uniform inside the solenoid. 15
Workbook: Chapter 24, Question 11 16
Calculating the Magnetic Field Due to a Current The magnetic field due to a long, straight conductor with a steady current has a magnitude given by μ I B= 0, 2π r where r is the perpendicular distance from the wire to the point at which the field is to be calculated and I is the current in the wire. μ 0 is a physical constant. Its value is 4π 10 7 T m/a. I r 17
Calculating the Magnetic Field Since the magnetic field is a vector, the magnetic field values at a given point in space due to different currents add together vectorially to give the net magnetic field at that point. 18
Workbook: Chapter 24, Question 12 19
KJF Textbook, Chapter 24, Problem 6 P24.6. Prepare: Assume the wires are infinitely long. First, determine the direction of the magnetic field due to the top and the bottom wire at points a, b, and c. The direction of the magnetic field is determined by the right-hand rule for each current wire. The net magnetic field direction is the vectorial sum of the fields B top and B bottom. Points a and c are at a distancer = 2 cm from both wires and point b is at a distancer = 1cm. Solve: According to the right-hand rule, the direction of all three magnetic fields points to the right. For all points, the vertical components of the two magnetic fields cancel. Therefore, we only are concerned about the horizontal components of the fields. The magnitude of the magnetic fields at points a, b, and c are: B a = B to p + B bottom = μ I 0 top 2πr a = 2 μ I 0 B b cos 45 + μ 0 I bottom 2πr a cos45 (cos45 ) = 2 (4π 10 7 T m/a)(10 A) 2πr a 2π ( 2 10 2 m) = B to p + B bottom = μ 0 I to p 2πr b B c = B to p + B bottom = μ 0I top 2πr c 2 2 = 2.0 10 4 T + μ I 0 bottom = 2 (4π 10 7 T m/a)(10 A) 2πr b 2π(1 10 2 m) cos 45 + μ 0I bottom 2πr c cos 45 = 2 μ I 0 (4π 10 7T m/a)(10 A) (cos45 ) = 2 2πr a 2π ( 2 10 2 m) 2 2 = 2.0 10 4 T = 4.0 10 4 T Assess: Since the two currents are opposite to each other, the magnetic field strength between the two wires is stronger than if the two currents ran in the same direction. 20
Calculating the Magnetic Field for Current Loops and Solenoids At the center of a single circular current loop of radius R, the magnetic field is center μ I B= 0. I 2R Inside a solenoid of length L with N turns, the magnetic field is L B=μ I N 0. L 21
Group Problem Solving What is the direction and magnitude of the magnetic field at point P, at the center of the loop? I = 3.0 A, R = 4.0 cm. 22