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Exercise:
A ring with radius RO carries a uniformly distributed charge of QO. A qO po charge is placed on the ring's central axis. abcliste abc Calculate the force acting on the po charge for a distance dO from the ring. Compare the result with the result you would get using Coulomb's law. abc Show with a formal calculation that for large distances dgg R the expression for the force between the ring and the po charge approaches Coulomb's force law. abcliste

Solution:
abcliste abc The force between the charged ring and the po charge is see lecture notes: F FF kC &quadquadtimesfracQtimes qtimes dleftR^+d^right^/ F approx resultFP- Using Coulomb's law we find F_C FCF kCtimesfracQtimes qd^ FC approx resultFCP- This is percerrP larger than the correct result. Coulomb's law overestimates the result because it ases that the charge of the ring is concentrated at a distance d dO from the po charge which is smaller than the real distance. abc By factoring out d^ in the numerator we can write the force as F k_CfracQ q dd^leftR/d^+right^/ For Rgg d the ratio R/d is much less than so we can approximate the force as F &approx k_CfracQ q dd^leftright^/ FCF This is the expression for Coulomb's law. abcliste
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Exercise:
A ring with radius RO carries a uniformly distributed charge of QO. A qO po charge is placed on the ring's central axis. abcliste abc Calculate the force acting on the po charge for a distance dO from the ring. Compare the result with the result you would get using Coulomb's law. abc Show with a formal calculation that for large distances dgg R the expression for the force between the ring and the po charge approaches Coulomb's force law. abcliste

Solution:
abcliste abc The force between the charged ring and the po charge is see lecture notes: F FF kC &quadquadtimesfracQtimes qtimes dleftR^+d^right^/ F approx resultFP- Using Coulomb's law we find F_C FCF kCtimesfracQtimes qd^ FC approx resultFCP- This is percerrP larger than the correct result. Coulomb's law overestimates the result because it ases that the charge of the ring is concentrated at a distance d dO from the po charge which is smaller than the real distance. abc By factoring out d^ in the numerator we can write the force as F k_CfracQ q dd^leftR/d^+right^/ For Rgg d the ratio R/d is much less than so we can approximate the force as F &approx k_CfracQ q dd^leftright^/ FCF This is the expression for Coulomb's law. abcliste
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Attributes & Decorations
Branches
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Tags
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(2, default)
Points
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Language
ENG (English)
Type
Calculative / Quantity
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