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Example Problem

Example Problem. A particle with charge +2 nC (1 nanoCoulomb =10 -9 C) is located at the origi n. What is the electric field due to this particle at a location <-0.2,-0.2,-0.2> m ?. Solution: Distance and direction :. m. Example Problem. 2. The magnitude of the electric field :.

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Example Problem

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  1. Example Problem A particle with charge +2 nC(1 nanoCoulomb=10-9 C) is located at the origin. What is the electric field due to this particle at a location <-0.2,-0.2,-0.2> m? • Solution: • Distance and direction: m

  2. Example Problem 2. The magnitude of the electric field: 3. The electric field in vector form:

  3. Clicker Question 1 • A penny carrying a small amount of positive charge Qpexerts an electric force Fon a nickel carrying a large amount of positive charge Qnthat is a distance daway (Qn> Qp). Which one of the following is nottrue? • The electric force exerted on the penny by the nickel is also equal to F. • B. The number of electrons in the penny is less than the • number of protons in the penny. • C., if d is small compared to the size of the • coins. • D. , if d is large compared to the size of the • coins.

  4. Clicker Question 2 A positive and a negative charge are separated by a distance r, What are the directions of the forces on the charges? r +q1 -q2 What is the magnitude of the self-force?

  5. The Coulomb Force e0 = permittivity constant r + F21 r - + 2 + 2 F21 1 Force repulsive Force attractive 1 Force on “2” by “1” • The force exerted by one point charge on another acts along line joining the charges. • The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs.

  6. How Strong is the Coulomb Force

  7. Electric Field [N/C] Electric field has units of Newton per Coulomb:

  8. No ‘self-force’! Point charge does not exert field on itself!

  9. The Superposition Principle +q2 +q3 -q1 The net electric field at a location in space is a vector sum of the individual electric fields contributed by all charged particles located elsewhere. The electric field contributed by a charged particle is unaffected by the presence of other charged particles.

  10. The Superposition Principle +q2 +q3 -q1

  11. The E of a Uniformly Charged Sphere Can calculate using principle of superposition: for r>R (outside) for r<R (inside) Recall this every night before bed!

  12. The Superposition Principle s -q +q Example of electric dipole:HCl molecule The electric field of a dipole: Electric dipole: Two equally but oppositely charged point-like objects What is the E field far from the dipole (r>s)?

  13. Calculating Electric Field y s -q +q x z Choice of the origin Choice of origin: use symmetry

  14. 1. E along the x-axis s -q +q r

  15. Approximation: Far from the Dipole if r>>s, then While the electric field of a point charge is proportional to 1/r2, the electric field created by several charges may have a different distance dependence.

  16. 2. E along the y-axis y -q +q s

  17. 2. E along the y-axis y if r>>s, then at <0,r,0> -q +q s

  18. 3. E along the z-axis at <r, 0, 0> y at <0, r, 0> or <0, 0, r> z x Due to the symmetry E along the z-axis must be the same as E along the y-axis!

  19. Other Locations

  20. The Electric Field Point Charge: y - + x Dipole: for r>>s : at <r,0,0> z s at <0,r,0> -q +q at <0,0,r>

  21. Example Problem y A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 210-10 m along the x-axis. Calculate the magnitude of the E field at <0, 210-8, 0> m. E=? Since r>>s: 200Å x 2Å Using exact solution:

  22. Interaction of a Point Charge and a Dipole +Q +q -q s • Direction makes sense? - negative end of dipole is closer, so its net contribution is larger • What is the force exerted on the dipole by the point charge? - Newton’s third law: equal but opposite sign

  23. Dipole Moment x: r>>s y, z: The electric field of a dipole is proportional to the Dipole moment: p = qs , direction from –q to +q Dipole moment is a vector pointing from negative to positive charge

  24. Dipole in a Uniform Field Forces on +q and –q have the same magnitude but opposite direction It would experience a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field.

  25. Choice of System Multiparticle systems: Split into objects to include into system and objects to be considered as external. • To use field concept instead of Coulomb’s law we split the Universe into two parts: • the charges that are the sources of the field • the charge that is affected by that field

  26. A Fundamental Rationale • Convenience: know E at some location – know the electric force on any charge: • Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. Example: if E>3106 N/C air becomes conductor • Retardation • Nothing can move faster than light c • c = 300,000 km/s = 30 cm/ns Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<<c !!!

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