Three charged, concentric, partial-circle thin rings are placed with the origin of the coordinate system at their centers. The outer positively charged three-quarter-circle thin ring (shown in red) has a radius R3 ar a uniform linear charge density of Aa. The middle positively charged semi-circle thin ring (shown in blu has a radius R2 and a uniform linear charge density of 2. The inner positively charged quarter-circle th ring (shown in green) has a radius R1 and a uniform linear charge density of i. a. Calculate the total electric potential (i.e., voltage) at the "center" of the two rings. {Express your answer in terms of A , 2 , and ha.} YOU MUST SHOW ALL WORK AND CALCULATIONS TO GET CREDIT.NO EXCEPTIONS! b. If a positive point charge, q, is brought in from very far away and placed at the center of the ring, calculate the change in electric potential energy for the system. R3? R2 RI

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Chapter6: Gauss's Law
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Problem 49P: Determine if approximate cylindrical symmetry holds for the following situations. State why or why...
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Three charged, concentric, partial-circle thin rings are placed with the origin of the coordinate system at
their centers. The outer positively charged three-quarter-circle thin ring (shown in red) has a radius R3 and
a uniform linear charge density of A. The middle positively charged semi-circle thin ring (shown in blue)
has a radius R2 and a uniform lincar charge density of 2. The inner positively charged quarter-circle thin
ring (shown in green) has a radius R1 and a uniform linear charge density of i.
a. Calculate the total electric potential (i.e., voltage) at the “center" of the two rings.
{Express your answer in terms of A , d2 , and ha.}
YOU MUST SHOW ALL WORK AND CALCULATIONS TO GET CREDIT...NO EXCEPTIONS!
b. If a positive point charge, q, is brought in from very far away and placed at the center of the ring,
calculate the change in electric potential energy for the system.
R3?
R2
RI
Transcribed Image Text:Three charged, concentric, partial-circle thin rings are placed with the origin of the coordinate system at their centers. The outer positively charged three-quarter-circle thin ring (shown in red) has a radius R3 and a uniform linear charge density of A. The middle positively charged semi-circle thin ring (shown in blue) has a radius R2 and a uniform lincar charge density of 2. The inner positively charged quarter-circle thin ring (shown in green) has a radius R1 and a uniform linear charge density of i. a. Calculate the total electric potential (i.e., voltage) at the “center" of the two rings. {Express your answer in terms of A , d2 , and ha.} YOU MUST SHOW ALL WORK AND CALCULATIONS TO GET CREDIT...NO EXCEPTIONS! b. If a positive point charge, q, is brought in from very far away and placed at the center of the ring, calculate the change in electric potential energy for the system. R3? R2 RI
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