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Electric Field

Electric Field. Teacher: Aurora Comis. Content (Subject matter - What are my objectives? What are the learning outcomes?) Electric Fields Field lines Uniform Fields Nonuniform Fields Electric Flux and Gauss’s Law Capacitors Potential Energy.

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Electric Field

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  1. Electric Field Teacher: Aurora Comis

  2. Content (Subject matter - What are my objectives? What are the learning outcomes?) • Electric Fields • Field lines • Uniform Fields • Nonuniform Fields • Electric Flux and Gauss’s Law • Capacitors • Potential Energy • Communication (What language do we need working with the content? What Physics language will learners communicate during the lesson?) • Simple Present (Electric Field is….) • Present Perfect (We have measured ….) • Imperative (Let us consider…..) The 4 C’s • Cognition (What thinking skills are demanded to the learners?) • Repeating procedures • Ordering steps • Checking results • Handling formulas • Defining concepts • Making hypotheses, interpreting, judging and evaluating to solve problems • Culture (What are the cultural implications of the topic?) • Some historical background • Practical and technological implications

  3. Analogy The electric field is the space around an electrical charge just like a gravitational field is the space around a mass.

  4. Electric Field • Space around a charge. What is the difference?

  5. Electric Field Vector, E • E = F/ qo • qo , positive test charge (it serves to allow the electric force to be measured, but is not large enough to create a significant force on any other charges). • E is a vector quantity • Unit: N/C • E is analogous to the gravitational field, g, where g=F/m

  6. Earth 10 kg Earth’s surface Gravitational Fields: Review Recall that surrounding any object with mass, or collection of objects with mass, is a gravitational field. Any mass placed in a gravitational field will experience a gravitational force. We defined the field strength as the gravitational force per unit mass on any “test mass” placed in the field: g=F/ m. g is a vector that points in the direction of the net gravitational force; its units are N / kg. F is the vector force on the test mass, and m is the test mass, a scalar. g and F are always parallel. The strength of the field is independent of the test mass. For example, near Earth’s surface mg / m = g = 9.8 N / kg for any mass. Some fields are uniform (parallel, equally spaced fields lines). Nonuniform fields are stronger where the field lines are closer together. uniform field 98 N nonuniform field

  7. - Electric Fields: Intro Surrounding any object with charge, or collection of objects with charge, is a electric field. Any charge placed in an electric field will experience a electrical force. We defined the field strength as the electric force per unit charge on any “test charge” placed in the field: E=F/ q. E is a vector that points, by definition, in the direction of the net electric force on a positive charge; its units are N / C. F is the vector force on the test charge, and q is the test charge, a scalar. E and F are only parallel if the test charge is positive. Some fields are uniform (parallel, equally spaced fields lines) such as the field on the left formed by a sheet of negative charge. Nonuniform fields are stronger where the field lines are closer together, such as the field on the right produced by a sphere of negative charge. uniform field q + F nonuniform field - - - - - - - - - - - - - -

  8. Overview of Fields Charge, like mass, is an intrinsic property of an object. Charges produce electric fields that affect other charges; masses produce gravitational fields that affect other masses. Gravitational fields lines always point toward an isolated mass. Unlike mass, though, charges can be positive or negative. Electric field lines emanate from positive charges and penetrate into negative charge.We refer to the charge producing a field as a field charge. A group of field charges can produce very nonuniform fields. To determine the strength of the field at a particular point, we place a small, positive test charge in the field. We then measure the electric force on it and divide by the test charge: For an isolated positive field charge, the field lines point away from the field charge (since the force on a positive charge would be away from the field charge). The opposite is true for an isolated negative field charge. No matter how complex the field, the electric force on a test charge is always tangent to the field line at that point. The coming slides will reiterate these ideas and provide examples.

  9. Electric & Gravitational Fields Compared Gravity: Electric Force: Field strength is given by per unit mass or force per unit charge, depending on the type of field. Field strength means the magnitude of a field vector. Ex #1: If a +10 C charge is placed in an electric field and experiences a 50 N force, the field strength at the location of the charge is 5 N/C. The electric field vector is given by: E = 5 N/C, where the direction of this vector is parallel to the force vector (and the field lines). Ex #2: If a -10 C charge experiences a 50 N force, E = 5 N/C in a direction opposite the force vector (opposite the direction of the field lines).

  10. Drawing an E Field for a Point Charge Let’s use the idea of a test charge to produce the E field for an isolated positive field charge. We place small, positive test charges in the vicinity of the field and draw the force vector on each. Note that the closer the test charge is to the field charge, the greater the force, but all force vectors are directed radially outward from the field charge. At any point near the field charge, the force vector points in the direction of the electric field. Thus we have a field that looks like a sea urchin, with field lines radiating outward from the field charge to infinity in all direction, not just in a plane. The number of field lines drawn in arbitrary, but they should be evenly spaced around the field charge. Isolated, positive point charge and its electric field + + Test charges and force vectors surrounding a field charge

  11. + Single Positive Field Charge This is a 2D picture of the field lines that surround a positive field charge that is either point-like or spherically symmetric. Not shown are field lines going out of and into the page. Keep in mind that the field lines radiate outwards because, by definition, an electric field vector points in the direction of the force on a positive test charge. The nearer you get to the charge, the more uniform and stronger the field. Farther away the field strength gets weaker, as indicated by the field lines becoming more spread out.

  12. Single Negative Field Charge The field surrounding an isolated, negative point (or spherically symmetric) charge looks just like that of an isolated positive charge except the field lines are directed toward the field charge. This is because, by definition, an electric field vector points in the direction of the force on a positive test charge, which, in this case is toward the field charge. As before, the field is stronger where the field lines are closer together, and the force vector on a test charge is parallel to the field. -

  13. Point Charges of Different Magnitudes Let’s compare the fields on two separate isolated point charges, one with a charge of +1 unit, the other with a charge of +2 units. It doesn’t matter how many field lines we draw emanating from the +1 charge so long as we draw twice as many line coming from the +2 charge. This means, at a given distance, the strength of the E field for the +2 charge is twice that for the +1 charge. +2 +1

  14. Equal but Opposite Field Charges Pictured is the electric field produced by two equal but opposite charges. Because the charges are of the same magnitude, the field is symmetric. Note that all the lines that emanate from the positive charge land on the negative charge. Also pictured is a small positive charge placed in the field and the force vector on it at that position. This is the vector sum of the forces exerted on the test charge by each field charge. Note that the net force vector is tangent to the field line. This is always the case. In fact, the field is defined by the direction of net force vectors on test charges at various places. The net force on a negative test charge is tangent to the field as well, but it points in the opposite direction of the field. Link #1 Link #2 Link #3

  15. Equal but Opposite Field Charges (cont.) D C - + A B Here is another view of the field. Since the net force on a charge can only be in one direction, field lines never intersect. Draw the electric force on a positive charge at A, the electric field vector and B, and the electric force on a negative charge at C. The net force on a + charge at D charge is directly to the left. Show why this is the case by drawing force vectors from each field charge and then summing these vectors.

  16. Multiple Charges: How to Determine the Field To determine the field surrounding two field charges, Q1 and Q2, we pick some points in the vicinity and place test charges there (red dots). Q1 exerts a force on each, directly away from itself (blue vectors), as does Q2 (purple vectors). The resultant vectors (black) show the direction of the net electric force and define the direction of the electric field. The net force vector on each test charge is tangent to the E field there. If we place little a tangent segment parallel with the net force at each test charge and do this at many different points, we will build a picture of the electric field. The same procedure can be used regardless of the number of field charges. Q2 + Q1 +

  17. Two Identical Charges + + With two identical field charges, the field is symmetric but all field lines go to infinity (if the charges are positive) or come from infinity (if the charges are negative). As with any field the net force on a test charge is tangent to the field. Here, each field charge repels a positive test charge. The forces are shown as well as the resultant vectors, which are tangent to the field lines.

  18. Field Strengths: Point Charge; Point Mass Suppose a test charge q is placed in the electric field produced by a point-like field charge Q. From the definition of electric field and Coulomb’s law KQq/r2 KQ F E = = = q q r2 Note that the field strength is independent of the charge placed in it. Suppose a test mass m is placed in the gravitational field produced by a point-like field mass M. From the definition of gravitational field and Newton’s law of universal gravitation GMm/r2 GM F g = = = m m r2 Again, the field strength is independent of the mass place in it.

  19. Uniform Field Just as near Earth’s surface the gravitational field is approximately uniform, the electric field near the surface of a charged sphere is approximately uniform. A common way to produce a uniform E field is with a parallel plate capacitor: two flat, metal, parallel plates, one negative, one positive. Aside from some fringing on the edges, the field is nearly uniform inside. This means everywhere inside the capacitor the field has about the same magnitude and direction. Two positive test charges are depicted along with force vectors. - - - - - - - - + + + + + + + +

  20. + + Two + Field Charges of Different Magnitude • More field lines emanate from the greater charge; none of the field lines cross and they all go to infinity. • The field lines of the greater charge looks more like that of an isolated charge, since it dominates the smaller charge. • If you “zoomed out” on this picture, i.e., if you looked at the field from a great distance, it would look like that of an isolated point charge due to one combined charge. Although in this picture the greater charge is depicted as physically bigger, this need not be the case.

  21. Opposite Signs, Unequal Charges The positive charge has a greater magnitude than the negative charge. Explain why the field is as shown. (Answer on next slide.) - +

  22. Opposite Signs, Unequal Charges (cont.) - + More field lines come from the positive charge than land on the negative. Those that don’t land on the negative charge go to infinity. As always, net force on a test charge is the vector sum of the two forces and it’s tangent to the field. Since the positive charge has greater magnitude, it dominates the negative charge, forcing the “turning points” of the point to be closer to the negative charge. If you were to “zoom out” (observe the field from a distance) it would look like that of an isolated, positive point with a charge equal to the net charge of the system.

  23. Summary of Fields due to Unequal Charges You should be able to explain each case in some detail.

  24. The Electric Field If we know the electric field, we can calculate the force on any charge The direction of the force depends on the sign of the charge – in the direction of the field for a positive charge, opposite to it for a negative one.

  25. Electric Field Lines Electric field lines are a convenient way of visualizing the electric field and indicate its strength and its direction. Electric field lines: - Point in the direction of the field vector at every point - Electric field vectors are tangent to the curve. - Start at positive charges or infinity - End at negative charges or infinity - Are more dense where the field is stronger (The more dense the lines, the stronger the field) Simulation http://online.cctt.org/physicslab/content/applets/pointcharges/elefi_z.htm

  26. Electric Field Lines The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point towards the charge rather than away from it.

  27. Electric Field Lines

  28. Electric Field Lines Combinations of charges. Note that, while the lines are less dense where the field is weaker, the field is not necessarily zero where there are no lines. In fact, there is only one point within the figures below where the field is zero – can you find it?

  29. Conductors and Electric Fields (under electrostatic conditions) • “The electric field is zero inside a charged conductor”. • “Excess charge on an isolated conductor resides on the surface”. • “Excess charge accumulates on sharp points”. • Electric field lines meet the conductor perpendicular to the surface of the conductor.

  30. Shielding Where are you safe during a thunderstorm? • In a car or • Outdoors Why can you not get radio reception in a tunnel or in a steel bridge?

  31. Electric Field for a Point Charge Using E=F/qo and Coulomb’s Law prove: E = k Q ______ r2 where Q is the central charge.

  32. Electric Field http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

  33. Example 1 • A test charge of +3µC is located 5m to the east of a -4µC charge. • A) Find the electric force felt by the test charge. • B) Find the electric field at that location. • Answer: 4.32x10-3 N, 1.44 x 103 N/C along the –x axis.

  34. Example 2 • If a test charge is moved to a location three times as far as its original location, how does the electric field change?

  35. Example 3 • Calculate the electric field felt by a test charge located half way between a charge of +1C and a charge of -3C, that are 2m apart. • Answer: 1.8 x 1010 N/C

  36. Shielding and Charge by Induction Since excess charge on a conductor is free to move, the charges will move so that they are as far apart as possible. This means that excess charge on a conductor resides on its surface, as in the upper diagram.

  37. When electric charges are at rest, the electric field within a conductor is zero.

  38. The electric field is always perpendicular to the surface of a conductor – if it weren’t, the charges would move along the surface.

  39. _ _ _ _ _ _ + + + + + + Excess Charge on a Conductor Any excess charge placed on a conductor will immediately distribute itself over the surface of the conductor. No excess charge will remain inside. On a spherical conductor the excess charge will be distributed evenly. If electrons are added, they themselves will spread out. If electrons are removed, electrons in the conductor will replace them, leaving all excess positive charge on the surface. Excess charge placed on an insulator pretty much stays put. Now lets add some extra charges. _ _ _ _ The new charges repel themselves and reside only on the surface. _

  40. Excess Charge on a Pointy Conductor Excess charge, which always resides on the surface of a conductor, will collect in high concentrations at points. In general, the smaller the radius of curvature, R, the greater the charge density (charge per unit area). The reason for this is that when R is large, neighboring charges push a charge nearly tangent to the surface (left pic). But where R is small (as near a point), neighboring charges are mostly pushing a charge outward, away from the surface instead of away from each other (right pic). This allows the charges be reside closer together. vector forces due to neighboring charges _ _ _ _ _ _ _ _ _ _ _ _ _ _ smallR, high charge density _ _ _ _ _ _ _ _ _ _ _ largeR, low charge density _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

  41. Electric Fields In & Around Charged Conductors E is always zero inside any conductor, even a charged one. If this were not the case, mobile valence electrons inside the conductor would be accelerated by the E field, leaving them in a state of perpetual motion. Outside a charged conductor E is greater where the charge density is greater. Near points, E can be extremely high. Surrounding a sphere the field is radially symmetric, just the field due to a point charge. _ _ _ _ _ _ _ _ smallR, strong E _ _ _ _ _ _ _ _ _ _ _ _ E = 0inside _ E = 0inside _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ largeR, weak E

  42. The electric field is stronger where the surface is more sharply curved.

  43. Shielding Electric Fields A box or room made of metal or with a metal liner can shield its interior from external electric fields. Valence e-’s in the metal will respond to the field and reorient themselves until the field inside the box no longer exists. The external field (black) points right. This causes a charge separation in the box (e-’s migrating left), which produces its own field (red), negating the external field. Thus, the net field inside is zero. Outside, the field persists. - - - - + + + +

  44. A conductor can be charged by induction, if there is a way to ground it. This allows the like charges to leave the conductor; if the conductor is then isolated before the rod is removed, only the excess charge remains.

  45. Faraday Cage A Faraday cage or Faraday shield is a conductive enclosure that shields its contents from both static and non-static electrical fields. A Faraday cage's operation depends on the fact that an external static electrical field will cause the electrical charges within the cage's conducting material to redistribute themselves so as to cancel the field's effects in the cage's interior. This phenomenon is used, for example, to protect electronic equipment from lightning strikes and other electrostatic discharges.

  46. Electric Flux and Gauss’Law Electric flux is a measure of the electric field perpendicular to a surface

  47. Electric flux • The number of field lines (N) through a surface (A) is proportional to the electric field N~EA: • The ‘flux’ =EA • If the field lines make an angle with the surface: • =EAcos where  is the angle between the field lines and the normal to the surface • For field lines going through a closed surface (like a sphere), field lines entering the interior are negative and those leaving the interior are positive

  48. Gauss’ Law Consider a point charge q. Imagine a sphere with radius r surrounding the charge. The E-field and flux anywhere on the sphere are: It can be proven that this holds for any closed surface: Gauss’ Law

  49. Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface

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