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extra 2 - Chapter 21 6 21.1 What must the distance between...

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Chapter 21 21.1 What must the distance between point charge q 1 = 26 × 10 6 C and point charge q 2 = 47 × 10 6 C for the electrostatic force between them to be 5.70N? The magnitude of the force of attraction is given by Coulomb’s law where we have taken the absolute value of the force and the charges. F = q 1 q 2 4 πε 0 r 2 r = q 1 q 2 4 0 F = 26 × 10 6 C 47 × 10 6 C 4 0 5.7 N = 1.39 m 21.5 Of the charge Q, on a tiny sphere, a portion q is to is to be transferred to a second nearby sphere. The spheres can be treated as particles. For what value of q/Q maximizes the magnitude F of the electrostatic force between the two spheres. We begin with a drawing showing the charge on each sphere. r (Q-q) q To ±nd the maximum, we take the derivative and set it equal to zero. F = q ( Q q ) 4 0 r 2 = Qq q 2 4 0 r 2 dF dq = 0 = Q 2 q 4 0 r 2 q Q = 1 2 21.8 In Fig 21-23, four particles for a square. The charges are q 1 = q 4 = Q and q 2 = q 3 = q (a) What is Q / q if the net electrostatic force on particles 1 and 3 is zero. (b) Is there any value of q that makes the net electrostatic force on the each of the four particles zero? Explain.

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We begin by drawing the forces on 1 and 3. We know that the diagonal force will be repulsive and we know that the magnitude of the remaining forces are identical (since the charges are identical). To get them to all balance, the q and Q must have opposite signs. Q q Q q F 13 F 23 F 34 1 2 3 4 Q q Q q F 31 F 21 F 41 1 2 3 4 F 23 = q q 4 πε 0 2 a 2 cos45 ° ˆ i + q q 4 0 2 a 2 sin45 ° ˆ j F 34 = q Q 4 0 a 2 ˆ i F 13 = q Q 4 0 a 2 ˆ j F = 0 = F 23 + F 34 + F 13 0 = q q 4 0 2 a 2 ° + q Q 4 0 a 2 ˆ i + q q 4 0 2 a 2 °+ q Q 4 0 a 2 ˆ j x component 0 = q q 4 0 2 a 2 ° + q Q 4 0 a 2 q q 4 0 2 a 2 ° = q Q 4 0 a 2 Q q = ° 2 = 4 y component q q 4 0 2 a 2 °= q Q 4 0 a 2 Q q = ° 2 = 2 4 We should now check the forces on charge 1.
F 41 = Q Q 4 πε 0 2 a 2 cos45 ° ˆ i + Q Q 4 0 2 a 2 sin45 ° ˆ j F 21 = q Q 4 0 a 2 ˆ i F 31 = q Q 4 0 a 2 ˆ j F = 0 = F 41 + F 21 + F 31 0 = Q Q 4 0 2 a 2 ° + q Q 4 0 a 2 ˆ i + Q Q 4 0 2 a 2 °+ q Q 4 0 a 2 ˆ j x

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extra 2 - Chapter 21 6 21.1 What must the distance between...

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