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Electric Charges, Forces, and Fields

Electric Charges, Forces, and Fields. The atom. The atom has positive charge in the nucleus , located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction.

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Electric Charges, Forces, and Fields

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  1. Electric Charges, Forces, and Fields

  2. The atom The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction. The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without all that much difficulty.

  3. Electric Charge “Charge” is a property of subatomic particles. Facts about charge: • There are 2 types basically, positive (protons) and negative (electrons) • LIKE charges REPEL and OPPOSITE charges ATTRACT • Charges are symbolic of fluids in that they can be in 2 states, STATIC or DYNAMIC.

  4. Charge Charge comes in two forms, which Ben Franklin designated as positive (+) and negative(–). Charge is quantized. • The smallest possible stable charge, which we designate as e, is the magnitude of the charge on 1 electron or 1 proton. • We say a proton has charge of e, and an electron has a charge of –e. • e is referred to as the “elementary” charge. • e = 1.602 × 10-19Coulombs. • The coulomb is the SI unit of charge.

  5. Question • You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

  6. Charging and Discharging There are basically 2 ways you can charge something. • Charge by friction • Induction “BIONIC is the first-ever ionic formula mascara. The primary ingredient in BIONIC is a chain molecule with a positive charge. The friction caused by sweeping the mascara brush across lashes causes a negative charge. Since opposites attract, the positively charged formula adheres to the negatively charged lashes for a dramatic effect that lasts all day.”

  7. Induction and Grounding The second way to charge something is via INDUCTION, which requires NO PHYSICAL CONTACT. We bring a negatively charged rod near a neutral sphere. The protons in the sphere localize near the rod, while the electrons are repelled to the other side of the sphere. A wire can then be brought in contact with the negative side and allowed to touch the GROUND. The electrons will always move towards a more massive objects to increase separation from other electrons, leaving a NET positive sphere behind.

  8. Electric Fields By definition, the are “LINES OF FORCE” Some important facts: • An electric field is a vector • Always is in the direction that a POSITIVE “test” charge would move • The amount of force PER “test” charge If you placed a 2nd positive charge (test charge), near the positive charge shown above, it would move AWAY. If you placed that same charge near the negative charge shown above it would move TOWARDS.

  9. Field Vectors from Field Lines • The electric field at a given point is not the field line itself, but can be determined from the field line. • The electric field vectors is always tangent to the line of force at that point. • Vectors of any kind are never curvy!

  10. Field Vectors from Field Lines - +

  11. Field Vectors from Field Lines - -

  12. Field between charged plates +++++++++++++++++++++++ ------------------------------------------

  13. Excess Charges on Conductors • Where does the excess charge reside on a charged conductor? (Van de Graf Generator)

  14. Field within a Conductor • When the electric charges are at rest, the electric field within the conductor is zero.

  15. Electric Fields at Conductor Surfaces Electric field lines contact conductor surfaces a right angles.

  16. Sample Problem: A certain static discharge delivers -0.5 Coulombs of electrical charge. How many electrons are in this discharge?

  17. Why use fields? • Fields exist even if no force is present. • The field of one particle only can be calculated. • Forces exist only when two or more particles are present.

  18. Electric Fields and Newton’s Laws Once again, the equation for ELECTRIC FIELD is symbolic of the equation for WEIGHT just like coulomb’s law is symbolic of Newton’s Law of Gravitation. The symbol for Electric Field is, “E”. And since it is defined as a force per unit charge he unit is Newtons per Coulomb, N/C. NOTE: the equations above will ONLY help you determine the MAGNITUDE of the field or force. Conceptual understanding will help you determine the direction. The “q” in the equation is that of a “test charge”.

  19. Electric Force • Charges exert forces on each other. • Like charges (two positives, or two negatives) repel each other, resulting in a repulsive force. • Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

  20. Electric Forces and Newton’s Laws Electric Forces and Fields obey Newton’s Laws. Example: An electron is released above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel out the gravitational force on it. How far below the first electron is the second? Fe e mg r = ? 5.1 m e

  21. Coulomb’s Law – form 1 • Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them. • Coulomb’s law applies directly only to spherically symmetric charges.

  22. k = 8.99 × 109 N m2 / C2 • q1, q2 are charges (C) • r is distance between the charges (m) • F is force (N)

  23. Electric Force The electric force between 2 objects is symbolic of the gravitational force between 2 objects. RECALL:

  24. Coulomb’s Law – form 2 • Sometimes you see Coulomb’s Law written in a slightly different form • eo= 8.85 × 10-12 C2/ N m2 • q1, q2 are charges (C) • r is distance between the charges (m) • F is force (N) • This version is theoretically derived and less practical that form 1

  25. Sample Problem: A point charge of positive 12.0 μC experiences an attractive force of 51 mN when it is placed 15 cm from another point charge. What is the other charge? q1 = 12 x 10-6 C F = 51 x 10-6 N r = .15 m K = 8.99 x 109 F = k q1 q2 r2 Fr2 / kq1 = q2 q2 = (51 x 10-6 N)(.15 m)2 12 x 10-6 Q2 =

  26. Superposition • Electrical force, like all forces, is a vector quantity. • If a charge is subjected to forces from more than one other charge, vector addition must be performed. • Vector addition to find the resultant vector is sometimes called superposition.

  27. Force from Electric Field • The force on a charged particle placed in an electric field is easily calculated. • F = E q • F: Force (N) • E: Electric Field (N/C) • q: Charge (C)

  28. Sample Problem: The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg Styrofoam bead bearing 600 excess electrons when placed in the field? E = 4000 N/C m= 400 x 10-6 q= 600 x 1.6 x 10-19 = 9.6 x 10-17 C) F = Eq = (4000 N/C)(9.6 x 10-17 C) F = 3.84 x 10-13 N

  29. Sample Problem: A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration. • SF = Eq = ma • v =440 m/s • E = 5400 N/C • q= 1.6 x 10-19 C • m= 1.67 x10-27 kg • Eq/m = a • (5400 N/C)(1.6 x 10-19 ) = 5.17 x1011 m/s21.67 x10-27 kg x10-27 kg

  30. For Spherical Electric Fields • The Electric Field surrounding a point charge or a spherical charge can be calculated by: • E = k q / r2 • E: Electric Field (N/C) • k: 8.99 x 109 N m2/C2 • q: Charge (C) • r: distance from center of charge q (m) • Remember that k = 1/4peo

  31. Sample Problem: A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

  32. Sample Problem: A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

  33. Sample Problem: A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?

  34. Sample Problem: A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?

  35. Electric Fields and Forces AP Physics B

  36. Electric Forces and Vectors Electric Fields and Forces are ALL vectors, thus all rules applying to vectors must be followed. Consider three point charges, q1 = 6.00 x10-9 C (located at the origin), q3= 5.00x10-9 C, and q2 = -2.00x10-9 C, located at the corners of a RIGHT triangle. q2 is located at y= 3 m while q3 is located 4m to the right of q2. Find the resultant force on q3. Which way does q2 push q3? Which way does q1 push q3? 4m q2 q3 3m Fon 3 due to 1 5m q q1 Fon 3 due to 2 q = 37 q3 q= tan-1(3/4)

  37. Example Cont’ 4m q2 q3 3m Fon 3 due to 1 5m q q1 F3,1sin37 Fon 3 due to 2 q = 37 q= tan-1(3/4) q3 F3,1cos37 5.6 x10-9 N 7.34x10-9 N 1.1x10-8 N 64.3 degrees above the +x

  38. Example An electron and proton are each placed at rest in an external field of 520 N/C. Calculate the speed of each particle after 48 ns 8.32 x10-19 N 9.13x1013 m/s/s 4.98 x1010 m/s/s 4.38 x106 m/s 2.39 x103 m/s

  39. An Electric Point Charge As we have discussed, all charges exert forces on other charges due to a field around them. Suppose we want to know how strong the field is at a specific point in space near this charge the calculate the effects this charge will have on other charges should they be placed at that point. TEST CHARGE POINT CHARGE

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