phys1002_sln01_sm2_2007

phys1002_sln01_sm2_2007 - PHYS1002 TUTORIAL 1 SOLUTIONS...

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1 PHYS1002 TUTORIAL 1 SOLUTIONS Semester 2, 2007 1. COULOMB’S LAW (a) The magnitude of the force between two point charges Q 1 and Q 2 separated by a distance r is given by the Coulomb law which states that 1 2 2 kQ Q F r = where k is the “Coulomb’s constant”. In this question, we are told that the total charge on the two spheres is 1 μ C, lets call it q for generality. Because of this we know that 1 2 Q Q q = . Thus we have that 1 2 Q q Q = - . Putting this together with the Coulomb law gives 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ( ) . ( ) . 0. kQ Q k q Q Q F r r r F q Q Q qQ Q k r F Q qQ k - = = = - = - - + = This equation can be solved using the quadratic formula to give 2 2 2 2 6 6 2 9 2 1 4 4(0.15) 1.05 10 1 10 (1 10 ) 9 10 2 2 0.97 0.03 . 0.03 0.97 . r F q q k Q C or C Q C or C - - - × × ± - × ± × - × = = = μ μ = μ μ This means that one sphere has 0.03 μC of charge on it while the other has 0.97 μC of charge on it. (b) When the electroscope is charged, an equal amount of charge is transferred to each of the balls, which repel each other causing the leaves to make an angle of 45º with the vertical. Thus the horizontal forces keeping the balls apart and hence the leaves are held apart because of Coulomb forces due to each charged ball. Also, we have to remember that there will consequently be some tension in the leaves of the electroscope which are held at an angle to the vertical. In addition, we have to take into account the weight of the balls as they have a finite mass. Thus there are a number of forces acting on the system which need to be resolved in this problem.
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2 Let us now resolve all the forces in the x and y directions. 0 x F = , Thus 1 2 sin( ) T F F θ = = and 0 y F = so that cos( ) T mg θ = .
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