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The Electric Field Early scientists and philosophers struggled with the idea of “action at a distance”. How was the electric force propagated? Michael Faraday proposed that a “field” extended outwards from all charged objects, and that these fields interacted with one another. Fields are a great mathematical convenience. Faraday 1791-1897 The Field can be visualized mentally, graphically, and actually seen under certain circumstances…… Before TV there was no Nova, or Discovery Channel…. Michael Faraday popularized public lectures about cutting edge science. Here he is giving one of his famous Christmas Lectures at the Royal Institution in London, 1856 Visualizing the Electric Field These figures are from the book “Conceptual Physics” by Paul Hewitt • This is a photograph of a tank of oil (an electrical insulator) with millions of tiny cotton fibers (insulating and non-magnetic) suspended in it. • In the center is a metal object that is electrically charged • The cotton fibers mysteriously align themselves pointing radially outward from the charge. • Nothing is touching them, and they are not touching each other • “Something” with Faraday decided to call “The Electric Field” is reaching out through space and moving the fibers. Visualizing Electric Fields: A Single Point-Charge The number of field lines starting on a positive charge (or ending on a negative charge) is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together. Field lines trace the direction that a tiny positive “test charge” would move if placed at that location. Visualizing Electric Fields: Two Charges The lines emanating from two equal charges, opposite in sign will connect to form a Dipole (two poles). While if the charges are the same, the lines will avoid each other, and the charges repel ConcepTest 16.12a Electric Field Lines I 1) What are the signs of the charges whose electric fields are shown at right? 2) 3) 4) 5) no way to tell ConcepTest 16.12a Electric Field Lines I 1) What are the signs of the charges whose electric fields are shown at right? 2) 3) 4) 5) no way to tell Electric field lines originate on positive charges and terminate on negative charges. ConcepTest 16.12b Electric Field Lines II Which of the charges has the greater magnitude? 1) 2) 3) Both the same ConcepTest 16.12b Electric Field Lines II Which of the charges has the greater magnitude? 1) 2) 3) Both the same The field lines are denser around the red charge, so the red one has the greater magnitude. Follow-up: What is the red/green ratio of magnitudes for the two charges? Math Definition of Electric Field The electric field E is the vector describing the force exerted by a single charge or distribution of charges, per unit charge. F = Eq The definition assumes that the field can be calculated anywhere, by computing the force exerted on a tiny “test charge” so small that it doesn’t add its own field to the mix Calculating the Electric Field For a point charge Q, we calculate its Electric Field using an imaginary (minute) test charge “q”: Since the force between 2 charges is given by Coulomb's law, the force felt by our tiny test charge q would be F = k Qq/r2 F=Eq E= F/Q Where the Electric field is (units of newton per coulomb) = k Q/r2 This is similar to the way we simplify the law of gravitation for everyday situations, by finding ‘g’ and then simply using F = mg ConcepTest 16.8a Field and Force I Between the red and the blue charge, which of them experiences the greater electric field due to the green charge? +1 d +2 1) +1 2) +2 3) the same for both +1 d +1 ConcepTest 16.8a Field and Force I Between the red and the blue charge, which of them experiences the greater electric field due to the green charge? +1 d 1) +1 2) +2 3) the same for both +2 Both charges feel the same electric field due to the green charge because they are at the same point in space! +1 d +1 Q E=k 2 r Using Coulomb’s Law for Multiple Charges Coulomb’s law strictly describes point charges. Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors. The net force on a charge is the vector sum of all the forces acting on it. Where would this sort of thing be important? 1 ConcepTest 16.6 Forces in 2D 2 3 Which of the arrows best 4 represents the direction of the net force on charge +2Q d +Q +Q due to the other two charges? d +4Q 5 1 ConcepTest 16.6 Forces in 2D 2 3 Which of the arrows best 4 represents the direction of the net force on charge +2Q d +Q +Q due to the other two d charges? +4Q The charge +2Q repels +Q towards the right. The charge +4Q repels +Q upwards, but with a stronger force. Therefore, the net force is up and to +2Q the right, but mostly up. Follow-up: What happens if the yellow charge would be +3Q? +4Q 5 Vector Electric Field Calculation See Example 16.9 in the book Find the Direction and Magnitude of the Electric Field due to a a pair of unequal Charges. (takes 10 min, a good recap on using vectors.) We can go over this in recitation ConcepTest 16.9c Superposition III -Q +Q What is the direction of the electric field at the position of the X ? 2 3 1 4 +Q 5 ConcepTest 16.9c Superposition III -Q +Q What is the direction of the electric field at the position of the X ? 2 3 1 4 +Q 5 The two +Q charges give a resultant E field that is down and to the right. The –Q charge has an E field up and to the left, but smaller in magnitude. Therefore, the total electric field is down and to the right. Follow-up: What if all three charges reversed their signs? More Complex Field Lines and Symmetry • The electric field between two closely spaced, oppositely charged parallel plates is constant. • Where might this configuration occur? Shielding of Electric Field by a Conducting Enclosure - in this case a Metal Ring Charged Rod Metal Ring Note the field lines are due to induced charge only Look inside the ring: there are no lines! Figure taken from the book “Conceptual Physics” by Paul Hewitt Proof that the Electric Field is Zero Everywhere inside a Conductor - Think about how the electric field depends on Charge and Distance. EA=kQA/r12 and EB=kQB/r22 Step 1. Compare the distances, for convenience: r2 = 2r1 r2/r1 = 2 - A QB/QA = AreaB/AreaA =4 - r1 P - r2 - B - (r2/r1)2 = 4 Step 2. Compare the charges: - - - Step 3. Combine. Result: EB/EA = kQB/r22 kQA/r12 The test charge feels equal opposite fields from all directions -> No net field = 4/4 =1 Charge on the Earth according to Coulomb’s Law Electric Field at the Earth’s Surface is about E = 150 N/C, and points toward Earth’s center. We can assume the Earth’s net charge resides at the center and use coulomb’s law to find out how big it is: Definition of Electric Field: E=kQ/r2 Rearrange for Q: Q=Er2/k = 150 * (6373x103)2 / 9x109 = 680,000 C Where does this charge come from? The E-field surrounding a charged sphere is indistinguishable from that of a point charge (Which is also true of a gravitational field) Electricity in Lightning, Thunderstorms Raindrops and ice crystals charged by friction as they travel up and down inside the cloud segregate, causing an electric field. The ground below becomes charged by induction When the electric field gets strong enough, the air “breaks down” and becomes conductive, causing lightning to strike Globally, ~2000 on-going thunderstorms cause about 100 lightning strikes to earth each second. Electric Fields and Conductors The static electric field inside a conductor is zero. The free charges “instantly” align themselves to totally cancel the external field. The net charge on a conductor is all on its surface. -Charges want to be as far apart as possible. The is NO Electric field inside the car! (has nothing to do with tire rubber) This result is known as the Faraday Cage Another Example - Lighting Rods Rods focus the induced electric field that appears in the ground beneath the thunderstorm. With two consequences: 1. Charge can leak away through the air 2. If a breakdown occurs, the stroke will hit the rod and be carried into the ground, protecting nearby areas. Annually in the USA lightning causes more than 26,000 fires with damage to property in excess of $5-6 billion. Summary of Chapter 16 • Two kinds of electric charge – positive and negative • Charge is conserved • Charge on electron: • Conductors: electrons free to move • Insulators: nonconductors • Semiconductors - insulators that conduct in response to electric field • Objects can be charged by conduction or induction • Coulomb’s law: very strong compared to all other forces. • Electric field is force per unit charge: • Electric field can be represented by electric field lines • Static electric field inside conductor is zero; surface field is perpendicular to surface • Gauss’s law: The Electric Field Surrounding Two Charges 1. A Negative, B Positive 2. Both Negative 3. Both Positive 4. A Positive, B Negative 1. A Negative, B Positive A B 2. Both Negative 3. Both Positive 4. Cannot tell Application of Electrostatics: Photocopy Machines What special property must the roller have? And the toner particles? What about the paper? Photocopy Machines and Computer Printers Use Electrostatics Laser printer is similar, except a computer controls the laser intensity to form the image on the drum