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exam1_sol_009

# exam1_sol_009 - PHY2049 Fall 2009 Profs A Petkova A Rinzler...

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PHY2049 Fall 2009 Profs. A. Petkova, A. Rinzler, S. Hershfield Exam 1 Solution 1. Two identical conducting spheres A and B carry identical charges. They are separated by a distance much larger than their diameters. The magnitude of the electrostatic force between the spheres is F . One of the spheres is connected to earth ground and then disconnected from earth ground. The spheres are now allowed to touch and then separated to their original distance. The magnitude of the electrostatic force between the spheres is now: Answer: 1 4 F Solution: Let the charge on each sphere be Q inititally. The magnitude of the force between the spheres is F = kQ 2 /r 2 , where r is their separation. When the sphere is grounded, its charge becomes zero. After the spheres touch, they each have charge Q/ 2. Thus, the magnitude of the force between them after they are again placed at separation r is k ( Q/ 2) 2 /r 2 = F/ 4. 2. For the arrangement of the electron and two protons shown in each case rank the magnitude of the net electrostatic force on the electron, greatest first. Answer: ( a ) > ( c ) > ( b ) Solution: The magnitude of the force on the electron in case (a) is greater than the magnitude of the force in (b) because because in (a) the forces from the two protons add, while in (b) they subtract: F a > F b . In case (c) one of the protons is further away at a distance of d 2 + D 2 . The forces are not opposed as in case (b) so F c > F b . On the other hand because the one charge is further away in case (c) the force in case (c) must be smaller than in (a): F a > F c . 3. As shown in the Figure, a charge of q = 3 C lies at the origin surrounded by a spherical shell of charge having a fixed surface charge density of σ = 15 μ C/m 2 . The shell has a radius R = 10 km. Where the shell crosses the x axis there is a hole (greatly exaggerated in the Figure) of 0.5 m 2 area. What vector force does the charge q experience from the shell? (Hint: remember that electrostatic forces obey superposition and consider if there is charge on the shell that is uncompensated.) Answer: 2 × 10 3 N ˆ i Solution: The hole has no charge. One way to make a neutral region is to take a completely positively charged shell and add a region of negative charge that cancels the positive charge. Thus, the force due to a shell with a hole is the same as that of a positively charged shell with no hole and a negatively charged region where the hole is. The force at the center of a positively charged shell is zero so the net force at the center is just due to the negatively charged region. That region has charge ( - 15 μC/m 2 )(0 . 5 m 2 ) = - 7 . 5 μC . The 3 C charge is attracted to this negative charge so the force is in the ˆ i direction. The magnitude of the force is k (3 C )(7 . 5 μC ) / (10 4 m ) 2 .

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4. A charge of - 3 . 0 nC lies fixed at the origin and a charge of +10 nC lies along the x axis fixed at x = 2 . 0 m. Where along the x axis will an arbitrary charge experience no net electrostatic force from the two fixed charges?
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exam1_sol_009 - PHY2049 Fall 2009 Profs A Petkova A Rinzler...

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