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# Electric Force and Field

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### Electric Force and Field

1. 1. Electric Force and Field Force <ul><li>What? -- Action on a distance </li></ul><ul><li>How? – Electric Field </li></ul><ul><li>Why? – Field Force </li></ul><ul><li>Where? – in the space surrounding charges </li></ul>September 18, 2007
2. 2. Vector Field Due to Gravity <ul><li>When you consider the force of Earth’s gravity in space, it points everywhere in the direction of the center of the Earth. But remember that the strength is: </li></ul><ul><li>This is an example of an inverse-square force (proportional to the inverse square of the distance). </li></ul>September 18, 2007 m M
3. 3. Idea of Test Mass <ul><li>Notice that the actual amount of force depends on the mass, m : </li></ul><ul><li>It is convenient to ask what is the force per unit mass. The idea is to imagine putting a unit test mass near the Earth, and observe the effect on it: </li></ul><ul><li>g(r) is the “gravitational field.” </li></ul>September 18, 2007
4. 4. Electric Field <ul><li>Electric field is said to exist in the region of space around a charged object: the source charge . </li></ul><ul><li>Concept of test charge : </li></ul><ul><ul><li>Small and positive </li></ul></ul><ul><ul><li>Does not affect charge distribution </li></ul></ul><ul><li>Electric field: </li></ul><ul><ul><li>Existence of an electric field is a property of its source; </li></ul></ul><ul><ul><li>Presence of test charge is not necessary for the field to exist; </li></ul></ul>September 18, 2007 + + + + + + + + +
5. 5. Electric Field <ul><li>A test charge of +3 µC is at a point P where an external electric field is directed to the right and has a magnitude of 4 × 10 6 N/C. If the test charge is replaced with another test charge of – 3 µC, what happens to the external electric field at P ? </li></ul><ul><li>A. It is unaffected. </li></ul><ul><li>B. It reverses direction. </li></ul><ul><li>C. It changes in a way that cannot be determined. </li></ul>September 18, 2007
6. 6. Electric Field September 18, 2007 <ul><li>Magnitude: E=F/q 0 </li></ul><ul><li>Direction: is that of the force that acts on the positive test charge </li></ul><ul><li>SI unit: N/C </li></ul>Situation Value Inside a copper wire of household circuits 10 -2 N/C Near a charged comb 10 3 N/C Inside a TV picture tube 10 5 N/C Near the charged drum of a photocopier 10 5 N/C Electric breakdown across an air gap 3 × 10 6 N/C At the electron’s orbit in a hydrogen atom 5 × 10 11 N/C On the suface of a Uranium nucleus 3 × 10 21 N/C
7. 7. 2. Which diagram could be considered to show the correct electric force on a positive test charge due to a point charge? September 18, 2007 A. B. C. D. E.
8. 8. Electric Field due to a Point Charge Q September 18, 2007 <ul><li>Direction is radial: outward for +|Q| </li></ul><ul><li>inward for -|Q| </li></ul><ul><li>Magnitude: constant on any spherical shell </li></ul><ul><li>Flux through any shell enclosing Q is the same: E A A A = E B A B </li></ul>A B Q q 0
9. 9. Electric Field due to a group of individual charge September 18, 2007
10. 10. Electric Field Lines <ul><li>The electric field vector is tangent to the electric field line at each point. The line has a direction, indicated by an arrowhead, that is the same as that of the electric field vector. The direction of the line is that of the force on a positive test charge placed in the field. </li></ul><ul><li>The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. Thus, the field lines are close together where the electric field is strong and far apart where the field is weak. </li></ul>September 18, 2007
11. 11. Electric Field Lines <ul><li>The lines must begin on a positive charge and terminate on a negative charge. In the case of an excess of one type of charge, some lines will begin or end infinitely far away. </li></ul><ul><li>The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. </li></ul><ul><li>No two field lines can cross. </li></ul>September 18, 2007
12. 12. Electric Field <ul><li>3. Rank the magnitudes E of the electric field at points A, B, and C shown in the figure. </li></ul><ul><li>A) E C >E B >E A </li></ul><ul><li>B) E B >E C >E A </li></ul><ul><li>C) E A >E C >E B </li></ul><ul><li>D) E B >E A >E C </li></ul><ul><li>E) E A >E B >E C </li></ul>September 18, 2007 . C . A . B
13. 13. Motion of a Charged Particle in a Uniform Electric Field September 18, 2007 <ul><li>If the electric field E is uniform (magnitude and direction), the electric force F on the particle is constant. </li></ul><ul><li>If the particle has a positive charge, its acceleration a and electric force F are in the direction of the electric field E. </li></ul><ul><li>If the particle has a negative charge, its acceleration a and electric force F are in the direction opposite the electric field E. </li></ul>