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Chapter 15 Field Forces The Electric Field

Chapter 15 Field Forces The Electric Field. Lecture 15. 12 February 1999 Friday. Physics 112. The Four Fundamental Forces. Gravitational force Electro magnetic force Strong nuclear force Weak nuclear force. How different would life be if there were more ions around?.

zephania-benson
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Chapter 15 Field Forces The Electric Field

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  1. Chapter 15 Field Forces The Electric Field Lecture 15 12 February 1999 Friday Physics 112

  2. The Four Fundamental Forces • Gravitational force • Electromagnetic force • Strong nuclear force • Weak nuclear force

  3. How different would life be if there were more ions around? We’re used to living in a world dominated by gravity. Let’s compare the force of gravity between two protons to the electrostatic force: Fg = G mp mp / r2 Fe = k e e / r2 *Note how similar these two look!

  4. Concept Quiz! Gravitational vs Electrical Force

  5. Fe k e2 / r2 = Fg G mp2 / r2 Note: this should be a unit-less quantity. Right? (9 X 109 N m2/C2)(1.6 X 10-19C)2 = (6.7 X 10-11N m2/kg2)(1.67X10-27kg)2 Let’s now take the ratio of the electrostatic force to the gravitational force:

  6. Fe 2.3 X 10-28 C2/ C2 = Fg 1.9 X 10-64 kg2/ kg2 = 1.2 X 1036 !!!!!! Good thing most objects are neutral, eh?

  7. Recall... We said that like gravity, the electric force is a Field Force What does THAT mean?

  8. No! Not that kind of field!

  9. The Earth has a gravitational field. We experience its effects on a daily basis. In fact, we describe it with the quantity g = 9.81 m/s2 Question... Does the Earth’s gravity extend to the Moon’s surface?

  10. YES!!! But is that familiar expression for the Earth’s gravitational field still valid at the Moon’s surface?

  11. Of course not! That expression has been derived for conditions at the Earth’s surface. The more general expression for the Earth’s gravitational field is given by... The minus sign indicates that it is an attractive field that points toward the Earth’s center...

  12. Gravity (con't) The familiargis only one possible value of Ge. While G and me are constant, if we move away from the Earth (toward the moon, for example), the magnitude of Ge decreases like 1/r2. Gravity is a field force -- that is, a force that acts at a distance without requiring physical contact.

  13. Why? are you spending so much time on gravity?Didn’t we cover that last semester? Now that we have an expression for the gravitational field, we can determine the force on a given mass (like ourselves) from the expression:

  14. Yes, but.... Everything we just did with gravity we can do with electricity, too! (and I think our intuition about gravity is better…)

  15. The Electric Field An object with a charge (q) produces an electric field around it given by

  16. So, when we bring a second charge (q) into the neighborhood of an existing charge, the second charge will feel a force due to the electric field of the first charge. That force is given by….

  17. The superposition principle applies to the electric field, too! So…. The proof is rather straightforward…if you believe that the electrostatic force obeys the superposition principle...

  18. Electric Field Lines Since we have a hard time visualizing a field, it is useful to develop the concept of field lines. Electric Field Lines indicate the direction and magnitude of the electric field at any point in space.

  19. Electric Field Lines 1) Begin on positive charges 2) End on negative charges 3) Point from positive to negative charge 4) Are most dense where the electric field is the strongest. 5) Are the least dense where the electric field is the weakest.

  20. - + Field lines Far apart. Field lines close together. strong weak weak strong

  21. Looking at the electric field lines gives us a way to come to understand the 1/r2 nature of the expression for electrostatic force… Let’s start in the 2 dimensional world first.. What is the density of lines passing through the blue circle? 8/2prblue What about the green circle? 8/2prgreen

  22. So in flat-land, the density of lines goes down by 1/distance away from the convergence point of the lines. In the 3-D world we live in, we replace the circles of flat-land with spheres. The density of lines passing through surrounding shells will decrease like 1/distance2, since the surface area of a sphere is 4pr2

  23. Points in the direction from 1 to 2! Example: y q1 q2 q3 r1 r2 x q1 = -1 mC q2 = -2 mC q3 = +1 mC r1 = 1 m r2=2 m What is the Total Force on q2? 1) Start by calculating the electric field of charge q1 at the location of charge q2. (i.e.,in the -x direction)

  24. Points in the direction from 3 to 2! Example (con’t): y q1 q2 q3 r1 r2 x q1 = -1 mC q2 = -2 mC q3 = +1 mC r1 = 1 m r2=2 m What is the Total Force on q2? 2) Then examine the electric field of q3 at q2. (i.e.,in the -x direction)

  25. Example (con’t): y q1 q2 q3 r1 r2 x q1 = -1 mC q2 = -2 mC q3 = +1 mC r1 = 1 m r2=2 m What is the Total Force on q2? 3) Next, use the superposition principle to carefully add together the results. (i.e.,the electric field at the location of q2 pointsin the -x direction)

  26. Example (con’t): y q1 q2 q3 r1 r2 x q1 = -1 mC q2 = -2 mC q3 = +1 mC r1 = 1 m r2=2 m What is the Total Force on q2? 4) Finally, multiply by q2 to get the force... (i.e.,the electric force at the location of q2 pointsin the +x direction)

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