Physics 17 Part M Dr. Alward Elementary Facts Concerning Magnets Magnets have north and south poles. Like Poles Repel Unlike Poles Attract Magnetic Dipoles Magnets have two poles, one north, the other south. Bar magnets are magnetic dipoles. Magnetic dipole fields look just like the ones for electric dipoles. A compass needle is a miniature bar magnet, one end of which is north, and the other end of which is south. If a compass needle is placed anywhere in a magnetic field, it will align itself tangent to a magnetic field curve. The arrowhead end of a compass needle is the north pole. Bar Magnet Magnetic field arrows point from N to S. Magnetic Compass Needle parallel to magnetic field lines 1
Magnetic Field of Earth Magnetic Force on Moving Charges Use the right-hand rule to determine the direction of the force: Flatten palm, fingers, and thumb. Point thumb in the direction along which the positive charge is moving. Earth s north magnetic pole is located at Earth s south geographic pole, and vice-versa. The magnetic field intensity is symbolized as B, and is units of tesla (T). 1.0 T = 10,000 gauss (G) Near the ground, B = ½ G Twist flat hand until the fingers point in the direction of the magnetic field arrows. The palm faces in the direction of the force on the charge. If the charge is negative, the back of the hand faces in the direction of the magnetic force on the charge. Magnetic forces on a moving charge are always perpendicular to the direction of motion, as well as perpendiculr to the magnetic field direction. F = QvB (assumes velocity direction is perpendicular to the direction of the magnetic field line at that point) Earth s magnetic field arrows leave Antarctica, wrap around the Earth, and pass through the equatorial plane at an angle of 90 o. Electrically charged particles racing toward Earth from the Sun are prevented by magnetic forces from reaching the Earth's surface. The figure at the right is a view frm above Earth s Arctic region, with magnetic field arrows shown as circles with pin-point arrows coming out of the sheet. Approaching Earth is a proton from the Sun. Using the right-hand rule, the proton is deflected to the east. Electrons from the Sun would be deflected to the west. 2
Example A: Suppose such a magnetic field created in a laboratory points from floor to ceiling, and an electron is fired parallel to a wall you re facing, from your left to your right. In which direction will the electron be deflected? Answer: Away from you, toward the wall Example B: A proton is fired upward from the equator. In which direction will it be deflected? Answer: westward Example C: A proton at the equator is fired northward. In which direction will it be deflected? Answer: Charges moving parallel to magnetic field lines experience zero magnetic force. Example: The magnetic field in a laboratory points from ceiling to floor. At Point P, a proton is fired from left to right, parallel to the floor. The magnetic force is perpendicular to the direction of motion, always pointing to the center of the circular path around which the proton travels. F = ma evb = mv 2 /r r = mv/eb 3
Current-Carrying Loops: Equivalent to a Bar Magnet Rule: (Above) If current is counter-clockwise, you're looking at the "north" face of the magnet. (Above) If current is clockwise, you re looking at the south face of the magnet Magnetic Flux Let t = time it takes for the flux change to occur N = number of turns ΔΦ = Φ - Φo = BA - BoA ΔΦ = absolute value of flux change Φ = BA Units: tesla-meter 2 (T-m 2 ) When the flux through a wire loop changes over time, there is induced in the loop a voltage, and the loop acts just as if there were a battery in the wire driving current around the loop. The average voltage induced in the loop during the period of time the flux is changing is given by Faraday s Law : Vave = N ΔΦ /t When the flux stops changing, there is zero induced voltage. 4
Example: A wire coil of radius r = 0.60 m has 200 turns faces a magnetic field whose intensity changes from 2.0 T to 5.0 T in 3.5 seconds. What average voltage is induced in the coil during this time period? A = π (0.60) 2 = 1.13 m 2 ΔΦ = 1.13 (5.0) - 1.13 (2.0) = 3.39 T-m 2 N = 200 t = 3.5 s Vave = 200 (3.39)/3.5 = 194 volts Alternating Current Power Supplies Unlike batteries which direct current in one direction only from the battery (they re called direct-current (DC) power supplies), alternating current power supplies have current traveling clockwise around a circuit, then counterclockwise, then clockwise, and so on. Electric power supplied by power stations supply energy via alternating current (AC). At the right is a simple AC circuit. Note the symbol for an AC power supply is a circle with a sine-wave. 5
Transformers The transformer is an electric device that transforms low alternating current voltages into high alternating voltages, and transforms high alternating voltages into low alternating voltages. Transformer on telephone pole Changing current in the primary coil causes a changing magnetic field on the primary side of the transformer. That changing field extends around to the secondary coil, which causes a changing flux through the coil, which induces an AC voltage in the secondary coil. The secondary coil acts as if it were an AC power supply which it is. V1 = primary voltage V2 = secondary voltage N1 = number of turns in the primary coil N2 = number of turns in the secondary coil Transformer Equation V2 = (N2/N1) V1 AC power supply to primary coil is not shown. (These are the average voltages.) 6