negatively charged paddle touches the electroscope c The negatively charged

Negatively charged paddle touches the electroscope c

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negatively charged paddle touches the electroscope. (c) The negatively charged paddle is removed. (a) (b) (c)
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692 Chapter 21 Electrostatics connection is removed in Figure 21.11d. Now, when the paddle is moved away from the electroscope in Figure 21.11e, the electroscope is still positively charged (but with a smaller deflection than in Figure 21.11b). The same process also works with a positively charged paddle. This process is called charging by induction and yields an electroscope charge that has the opposite sign from the charge on the paddle. 21.5 Electrostatic Force—Coulomb’s Law The law of electric charges is evidence of a force between any two charges at rest. Experiments show that for the electrostatic force exerted by a charge q 2 on a charge q 1 , F 2 1 , the force on q 1 points toward q 2 if the charges have opposite signs and away from q 2 if the charges have like signs (Figure 21.12). This force on one charge due to another charge always lies on a line between the two charges. Coulomb’s Law gives the magnitude of this force as F k q q r = 1 2 2 , (21.6) where q 1 and q 2 are electric charges, r r r = 1 2 is the distance between them, and k = 10 N m C 9 2 2 8 99 . (21.7) is Coulomb’s constant . You can see that one Coulomb is a very large charge. If two charges of 1 C each were at a distance of 1 m apart, the magnitude of the force they would exert on each other would be 8.99 billion N. For comparison, this force equals the weight of 450 fully loaded space shuttles! The relationship between Coulomb’s constant and another constant, 0 , called the elec- tric permittivity of free space , is k = 1 4 0  . (21.8) Consequently, the value of 0 is 0 12 8 85 10 = C N m 2 2 . . (21.9) An alternative way of writing equation 21.6 is then F q q r = 1 4 0 1 2 2  . (21.10) As you’ll see in the next few chapters, some equations in electrostatics are more convenient to write with k , while others are more easily written in terms of 1/(4  0 ). Note that the charges in equations 21.6 and 21.10 can be positive or negative, so the product of the charges can also be positive or negative. Since opposite charges attract and like charges repel, a negative value for the product q 1 q 2 signifies attraction and a positive value means repulsion. Finally, Coulomb’s Law for the force due to charge 2 on charge 1 can be written in vec- tor form: F k q q r r r k q q r r 2 1 1 2 3 2 1 1 2 2 21 = = ( ) ˆ . (21.11) In this equation, r ˆ 21 is a unit vector pointing from q 2 to q 1 (see Figure 21.13). The negative sign indicates that the force is repulsive if both charges are positive or both charges are negative. In that case, F 2 1 points away from charge 2, as depicted in Figure 21.13a. On the other hand, if one of the charges is positive and the other negative, then F 2 1 points toward charge 2, as shown in Figure 21.13b.
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