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Use the following constants if necessary. Coulomb constant, k = 8.987 × 10°N m²/c². Vacuum permitivity, €0 = 8.854 x 10-12 F/m. Magnitude of the Charge of one electron, e = - 1.60217662 × 10 19C. Mass of one electron, m. = 9.10938356 x 10-31 kg. The gravitational acceleration near the surface of Earth g = 9.8 m/s?. Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb. ceiling L 92

Use the following constants if necessary. Coulomb constant, k = 8.987 × 10°N m²/c². Vacuum permitivity, €0 = 8.854 x 10-12 F/m. Magnitude of the Charge of one electron, e = - 1.60217662 × 10 19C. Mass of one electron, m. = 9.10938356 x 10-31 kg. The gravitational acceleration near the surface of Earth g = 9.8 m/s?. Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb. ceiling L 92

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Use the following constants if necessary. Coulomb constant, k = 8.987 × 10° N: m²/c². Vacuum permitivity, €0 = 8.854 x 10- 12 F/m. Magnitude of the Charge of one electron, e = - 1.60217662 × 10-19c. Mass of one electron, m. = 9.10938356 × 10-31 kg. The gravitational acceleration near the surface of Earth g = 9.8 m/s². Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb . ceiling L step 1: Two small identically charged conducting spheres 1 and 2 of equal mass are hung from a fixed support with non conducting threads of equal length as shown in the figure. Both the spheres have equal mass m, = m2 = m and equal charge q1 = 92 = q. Assume that the charge of each sphere is q = 28 nC, the length of the thread is L = 234 cm and the horizontal separation is X = 17 cm. The x and y directions are shown in the figure. You have the liberty to choose any point as the origin of your coordinate system. (Hint: You may find it convenient to choose q, or q, as the origin of your coordinate system.) step 2: Now, say we discharge sphere 2, without changing any other variables. Discharging means that the new charge of the sphere 2 is q, = 0. Explain what will happen in your script and answer the followings: א
Transcribed Image Text:Use the following constants if necessary. Coulomb constant, k = 8.987 × 10° N: m²/c². Vacuum permitivity, €0 = 8.854 x 10- 12 F/m. Magnitude of the Charge of one electron, e = - 1.60217662 × 10-19c. Mass of one electron, m. = 9.10938356 × 10-31 kg. The gravitational acceleration near the surface of Earth g = 9.8 m/s². Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb . ceiling L step 1: Two small identically charged conducting spheres 1 and 2 of equal mass are hung from a fixed support with non conducting threads of equal length as shown in the figure. Both the spheres have equal mass m, = m2 = m and equal charge q1 = 92 = q. Assume that the charge of each sphere is q = 28 nC, the length of the thread is L = 234 cm and the horizontal separation is X = 17 cm. The x and y directions are shown in the figure. You have the liberty to choose any point as the origin of your coordinate system. (Hint: You may find it convenient to choose q, or q, as the origin of your coordinate system.) step 2: Now, say we discharge sphere 2, without changing any other variables. Discharging means that the new charge of the sphere 2 is q, = 0. Explain what will happen in your script and answer the followings: א
ceiling //,/// Y L 93 92 x' step 3: Now say we insert another charged sphere 3 in between with a thread of length h which is shown in figure 2. Note that, value of h is the vertical distance from sphere 1 and 2 to the ceiling. Assume that the charge of sphere 3 is q3 = 3.5 nC. Find the separation after the system reaches equilibrium from this step. Hint: Use small angle approximation and if you use that then h → L. You may not be able to answer (d).(e) before you find (f), but finding expression for (d).(e) are necessary in order to find (f). d) Find the magnitude of electric force on q1 due to q2 and call it F2.1. magnitude of F2.1 Give your answer to at least three significance digits. e) Find the magnitude of electric force on q1 due to q3 and call it F3,1 magnitude of F3,1 Give your answer to at least three significance digits. N f) Find the separation after the system reaches equilibrium from step step 3:. equilibrium separation Give your answer to at least three significance digits.
Transcribed Image Text:ceiling //,/// Y L 93 92 x' step 3: Now say we insert another charged sphere 3 in between with a thread of length h which is shown in figure 2. Note that, value of h is the vertical distance from sphere 1 and 2 to the ceiling. Assume that the charge of sphere 3 is q3 = 3.5 nC. Find the separation after the system reaches equilibrium from this step. Hint: Use small angle approximation and if you use that then h → L. You may not be able to answer (d).(e) before you find (f), but finding expression for (d).(e) are necessary in order to find (f). d) Find the magnitude of electric force on q1 due to q2 and call it F2.1. magnitude of F2.1 Give your answer to at least three significance digits. e) Find the magnitude of electric force on q1 due to q3 and call it F3,1 magnitude of F3,1 Give your answer to at least three significance digits. N f) Find the separation after the system reaches equilibrium from step step 3:. equilibrium separation Give your answer to at least three significance digits.
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