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Announcements

Announcements. My office hours tomorrow are rescheduled: 2:00 – 3:30 p.m. Tutorials: Monday: 5:30 – 7:00 Tuesday: 6:00 – 7:30 Wednesday: 5:30 – 7:00 Thursday: 6:00 – 7:30

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Announcements

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  1. Announcements • My office hours tomorrow are rescheduled: 2:00 – 3:30 p.m. • Tutorials: • Monday: 5:30 – 7:00 • Tuesday: 6:00 – 7:30 • Wednesday: 5:30 – 7:00 • Thursday: 6:00 – 7:30 • --Tutorials are there to help you find a solution to the homework problems. They are not sessions for the TAs to work problems for you. • --Come to the sessions after serious attempts at the homework. • --TAs will watch your approach and provide guidance when you have problems.

  2. ke= 8.988109 Nm2/C2 Coulomb’s Law vs. Gravity A Helium nucleus (charge +2e) is separated from one of its electrons (charge –e) by about 3.00 10-11m, and we just calculated the electrostatic forces involved. • Suppose we could adjust the distance between the nucleus (considered as a point particle) and one electron. Can we find a point at which the electric and gravitational forces are equal? • Yes, move the particles apart. • Yes, move the particles together. • No, they will never be equal.

  3. + + – – – + + Small test charge q + Electric Fields • Electric Field is the ability to exert a force at a distance on a charge • It is defined as force on a test charge divided by the charge • Denoted by the letter E • Units N/C

  4. E-Field: Why? • When we have a charge distribution, and we want to know what effect they would have external charges, we can either • Do many sums (or integrations) every time a charge comes in to find the force on that charge • Or calculate the field from the charge distribution, and multiply the field by the external charge to obtain the force • Simplification!

  5. Point charge Q Small test charge q Electric Field from a Point Charge Note: the field is a vector!

  6. q2 = -2 C 10 cm E2 = 1.797  106 N/C Etot = 4.019106 N/C  = 26.6o 5 cm E1 = 3.595  106 N/C q1 = +1 C E-Field from two or more charges • Each charge creates its own Electric Field • Electric Fields must be added as a vector sum

  7. + – Negative Charge Positive Charge Electric Field from a Point Charge

  8. + + + + Electric Field from two Charges

  9. + - + - Electric Field from two Charges

  10. + + - - Electric Field Lines • Graphical Illustration of Electrical Fields • Lines start on positive charges and end on negative • Number of lines from/to a charge is proportional to that charge • Density of lines tells strength of field.

  11. Electric Field Lines Consider the four field patterns below: Assuming that there are no charges in the region of space depicted, which field pattern(s) could represent electrostatic field(s)?

  12. A cube with side 1 cm has a charge density of  = 1 C/m3. What is the charge of the cube? • 1 C • 0.01 C = 10 mC • 10-4 C = 100 m C • 10-6C = 1 mC 1 cm Charge Densities Charge can be localized to discrete points (point charges), or it may be spread out over a volume, a surface or a line • Charge density  units C/m3 • Surface charge density  units C/m2 • Linear charge density  units C/m

  13. Example 1: infinite line of charge Electric field a distance a away from an infinite line of charge? • Charge density λ units C/m. Hint: Use Maple if the integral is not obvious.

  14. General approach, continuous charge distributions • Write an expression for dE in terms of dq, r. • Express dq in terms of charge density and some coordinate element dx. • Express r in terms of the same coordinate or coordinates.

  15. Electric Fields and Forces

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