Electrical Fields
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The document discusses various topics relating to electrical fields including: - The definition of electric field strength and its relationship to charge and distance. - Electric field lines and the rules for drawing them, including that they originate from positive charges and terminate at negative charges. - How electric field strength decreases with distance from a charged object. - Examples of electric field drawings and practice problems identifying correct and incorrect field patterns. - The relationship between number/closeness of field lines and magnitude of electric charge. - Applying the principle of superposition to find the net electric force on charges from multiple sources. - The concept of electrostatic equilibrium for conductors.
Electrical Fields
- 1. Electrical Fields February 24th, 2009
- 2. Electric Field Strength Electric Field Region in space around a charged object in which a stationary charged object experiences an electric force because of its charge Depends on Charge and distance E = F electric / q 0 (see p. 643 in book) Substitute in for F electric (see p. 644) E = k c (q/r 2 )
- 3. Example An electrical field around a charged object is 5.95 x 10 6 N/C at a distance of 10.0 cm. Find the charge on the object
- 4. Electric Field Lines Lines that represent both the magnitude and direction of the electric field Number of lines is proportional to the electric field strength (more lines = stronger)
- 5. Rules for Drawing Line must begin at positive charge (or infinity) and must end at negative charge (or infinity) Number of lines is proportional to magnitude of the charge No two field lines from the same field can cross each other
- 6. Field Strength Field strength decreases as you move away from a charged object
- 7. Field Drawing with Two Charges Since forces are vectors the field strength is just the vector sum of both fields
- 9. Unequal Charges Can determine ratio of charge by seeing how many lines terminate
- 10. Electric Field Practice Problems Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams. Answer: C, D and E In C, the lines are directed towards a positively charged object. In D, the lines are not symmetrically positioned despite the fact that the object is a symmetrical sphere. In E, the lines are directed away from a negative charge.
- 11. Erin Agin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain. Electric field lines should never intersect each other. Erin crossed his lines.
- 12. Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____. Electric field lines are directed towards object A so object A must be negative. They are directed away from object B so object B must be positive.
- 13. Consider the electric field lines drawn at the right for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest. Answer: DAECB (with the order of C and B being in question) Electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart.
- 14. Use your understanding of electric field lines to identify the charges on the objects in the following configurations. Answer: Objects A, C, F, G, H and I are positive. Objects B, D and E are negatively charged. The principle is: electric field lines always approach negatively charged objects and are directed away from positively charged objects.
- 15. Observe the electric field lines below for various configurations. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge. Answer: B < A C < D G < E < F J < H < I The principle is that objects with the greatest charge will have the greatest number of lines emanating from it or approaching it.
- 16. Resultant Force When more than two charges are present often it is necessary to find the net electric force on one of them Coulomb’s law applies even when more than two charges are present Just find the forces acting on each charge and add (or subtract) This is the Principle of Superposition
- 17. Example Three charges are located on the x-axis. A 5.0 C charge is located at x=0.0 cm, a 1.5 C charge is located at x=3.0 cm and a -3.0 C charge is located at x=5.0 cm. Find the resultant force on the 5.0 C charge 21N
- 18. Practice Three charges are placed in a line: Find the net force on all three charges A B C -5 C -8 C 2 C 2 m 5 m
- 19. Conductors in Electrostatic Equilibrium Electrostatic equilibrium When no net motion of charge is occurring within a conductor Electrical field is 0 everywhere inside conductor Any excess charge resides entirely on the conductors outer surface Electrical field just outside a charge conductor is perpendicular to the conductor’s surface Charge tends to accumulate where the radius of curvature of the surface is smallest (sharp points)