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Exercise:
Two balls of mass mO are each susped from a LO long string to form a simple pulum. The two pula are placed such that the centers of the initally neutral balls are at a distance dO. The balls are then charged to QaO and QbO respectively. Determine the horizontal deflection of the two balls. center includegraphicswidth.textwidth#image_path:electric-pula# center H: Derive an for the horizontal displacement. There is no easy way to find a formal solution for this . You can solve it numerically e.g. using a tool like mathematica or graphically by plotting the two sides of the and finding the ersection.

Solution:
includegraphicswidthtextwidth#image_path:doublelectric-pulum-labelled# The vector of the two force vectors vecF_G gravitational force and vecF_C Coulomb force on a ball has to po in the direction of the string. Using similar triangles it follows: fracxy fracF_CF_G fracxsqrtL^-x^ frack_C Q_ Q_m g r^ frack_C Q_ Q_m g d+ x^ This complicated expression for x can be solved numerically e.g. using Mathematica or graphically. For the latter approach you can plot the graphs of the left and right hand side as a function of x in the same diagram using the numerical values for L k_C Q_ Q_ d m and g. The x-value at the ersection po corresponds to the solution. includegraphicswidthtextwidth#image_path:electric-pulum-plot-# The value read from the above diagram is xapprox .cm. A numercical solution using Mathematica leads to a value of x.cmapprox.cm.
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Exercise:
Two balls of mass mO are each susped from a LO long string to form a simple pulum. The two pula are placed such that the centers of the initally neutral balls are at a distance dO. The balls are then charged to QaO and QbO respectively. Determine the horizontal deflection of the two balls. center includegraphicswidth.textwidth#image_path:electric-pula# center H: Derive an for the horizontal displacement. There is no easy way to find a formal solution for this . You can solve it numerically e.g. using a tool like mathematica or graphically by plotting the two sides of the and finding the ersection.

Solution:
includegraphicswidthtextwidth#image_path:doublelectric-pulum-labelled# The vector of the two force vectors vecF_G gravitational force and vecF_C Coulomb force on a ball has to po in the direction of the string. Using similar triangles it follows: fracxy fracF_CF_G fracxsqrtL^-x^ frack_C Q_ Q_m g r^ frack_C Q_ Q_m g d+ x^ This complicated expression for x can be solved numerically e.g. using Mathematica or graphically. For the latter approach you can plot the graphs of the left and right hand side as a function of x in the same diagram using the numerical values for L k_C Q_ Q_ d m and g. The x-value at the ersection po corresponds to the solution. includegraphicswidthtextwidth#image_path:electric-pulum-plot-# The value read from the above diagram is xapprox .cm. A numercical solution using Mathematica leads to a value of x.cmapprox.cm.
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Attributes & Decorations
Branches
Electrostatics
Tags
coulomb, electrostatic
Content image
Difficulty
(4, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration