PHYS 1444 – Section 004 Lecture #13 RC Circuits RC Circuits Magnetism Magnetic Field Earth’s Magnetic Field Electric Current and Magnetism Directions in a Circular Wire? Magnetic Forces on Electric Current Magnetic Forces on Electric Current Magnetic Forces on Electric Current About the Magnetic Field, BExample 27 – 1 Example 27 – 2 Magnetic Forces on a Moving Charge Magnetic Forces on a Moving ChargeExample 27 – 3Monday, Mar. 26, 2007 1PHYS 1444-004, Spring 2007Dr. Andrew BrandtPHYS 1444 – Section 004Lecture #13Monday, Mar. 26 2007Dr. Andrew BrandtHW6 due Fri 3/30 at 8 pm•RC Circuits• Magnetism and Magnetic Field• Electric Current and Magnetism• Magnetic Force on Electric Currents• Magnetic Force on a Moving ChargeMonday, Mar. 26, 2007 2PHYS 1444-004, Spring 2007Dr. Andrew Brandt• Circuits containing both resistors and capacitors– RC circuits are used commonly in everyday life• Control windshield wiper• Timing of traffic light from red to green• Camera flashes and heart pacemakers• What does an RC circuit look like?– There should be a source of emf, capacitors and resistors• What happens when the switch S is closed?– Current immediately starts flowing through the circuit.– Electrons flow out of negative terminal of the emf source, through the resistor R and accumulate on the upper plate of the capacitor– The electrons from the bottom plate of the capacitor will flow into the positive terminal of the battery, leaving only positive charge on the bottom plate– As the charge accumulates on the capacitor, the potential difference across it increases– The current reduces gradually to zero -- at that point the voltage across the capacitor is the same as that of the emf– The charge on the capacitor increases until it reaches to its maximum C.RC CircuitsMonday, Mar. 26, 2007 3PHYS 1444-004, Spring 2007Dr. Andrew Brandt• What does all this look like graphically?– Charge on the capacitor and current as a function of time– From energy conservation (Kirchhoff’s 2ndrule), the emf must be equal to the voltage drop across the capacitor and the resistor• =IR+Q/C• R includes all resistance in the circuit, including the internal resistance of the battery, I is the current in the circuit at any instant, and Q is the charge of the capacitor at that same instantRC CircuitsMonday, Mar. 26, 2007 4PHYS 1444-004, Spring 2007Dr. Andrew BrandtMagnetism• So the magnet poles are the same as electric charge?– No. Why not?– While the electric charges (positive and negative) can be isolated the magnet poles cannot be isolated.– So what happens when a magnet is cut?• If a magnet is cut, two magnets are made.• The more they get cut, the more magnets are made– Single-pole magnets are called “monopoles,” but to date none have been observed…• Ferromagnetic materials: Materials that show strong magnetic effects– Iron, cobalt, nickel, gadolinium and certain alloys• Other materials show very weak magnetic effectsMonday, Mar. 26, 2007 5PHYS 1444-004, Spring 2007Dr. Andrew Brandt– 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 poles, magnetic field lines form closed loops, unlike electric field linesMagnetic 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 on 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, Mar. 26, 2007 6PHYS 1444-004, Spring 2007Dr. Andrew BrandtEarth’s Magnetic Field• 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 magnetic north pole• The Earth’s magnetic poles do not coincide with the geographic poles magnetic declination– Geomagnetic 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 of dipMonday, Mar. 26, 2007 7PHYS 1444-004, Spring 2007Dr. Andrew BrandtElectric 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 the current flows– Electric current produces a magnetic field• The first indication that electricity and magnetism are linked– 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, Mar. 26, 2007 8PHYS 1444-004, Spring 2007Dr. Andrew BrandtDirections in a Circular Wire?• OK, then what are the directions of the magnetic fields generated by the current flowing through circular loops?Monday, Mar. 26, 2007 9PHYS 1444-004, Spring 2007Dr. Andrew BrandtMagnetic 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 3rdlaw– This was also discovered 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 point in the direction of the current and the finger tips bend in the direction of magnetic field B, the direction of thumb points to the direction of the forceMonday, Mar. 26,
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