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*7. The electric potential energy of a uniformly charged square disk of length D and total charge is Q² UD 3.525- (c.g.s. units, approximate). The electric potential energy of a uniformly charged circular disk of radius R and total charge is UR (c.g.s. units, exact). a) Determine the relationships between the radius of the circle the length of a side of the small square and the length of a side of the big square, which are shown in the figure. 8 Q² = 3T R b) With the same surface charge density for all three surfaces (big square, circle and small square), rank the electric potential energies in increasing order of magnitude. Show all work.

*7. The electric potential energy of a uniformly charged square disk of length D and total charge is Q² UD 3.525- (c.g.s. units, approximate). The electric potential energy of a uniformly charged circular disk of radius R and total charge is UR (c.g.s. units, exact). a) Determine the relationships between the radius of the circle the length of a side of the small square and the length of a side of the big square, which are shown in the figure. 8 Q² = 3T R b) With the same surface charge density for all three surfaces (big square, circle and small square), rank the electric potential energies in increasing order of magnitude. Show all work.

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7. The electric potential energy of a uniformly charged square disk of length D and total charge is * Q² D UD≈ 3.525 (c.g.s. units, approximate). The electric potential energy of a uniformly charged circular disk of radius R and total charge is (c.g.s. units, exact). a) Determine the relationships between the radius of the circle the length of a side of the small square and the length of a side of the big square, which are shown in the figure. UR 8 Q² = *Extra credit (optional) 3T R b) With the same surface charge density for all three surfaces (big square, circle and small square), rank the electric potential energies in increasing order of magnitude. Show all work. c) What can you conclude about the electric potential energy of a circular disk compared to that of a square. Hint: If you called the circle's radius r, then the length of big square is 2r (the diameter of the circle) and the diagonal of the small square is also 2r (the diameter), so its length is √2r. We have the following areas: Big square: (2r)2 = 4r² Circle: Tr² Small square: 2r².
Transcribed Image Text:7. The electric potential energy of a uniformly charged square disk of length D and total charge is * Q² D UD≈ 3.525 (c.g.s. units, approximate). The electric potential energy of a uniformly charged circular disk of radius R and total charge is (c.g.s. units, exact). a) Determine the relationships between the radius of the circle the length of a side of the small square and the length of a side of the big square, which are shown in the figure. UR 8 Q² = *Extra credit (optional) 3T R b) With the same surface charge density for all three surfaces (big square, circle and small square), rank the electric potential energies in increasing order of magnitude. Show all work. c) What can you conclude about the electric potential energy of a circular disk compared to that of a square. Hint: If you called the circle's radius r, then the length of big square is 2r (the diameter of the circle) and the diagonal of the small square is also 2r (the diameter), so its length is √2r. We have the following areas: Big square: (2r)2 = 4r² Circle: Tr² Small square: 2r².
Expert Solution
Step 1

(a) From the figure, the diagonal of the small square is the diameter of the circle. 

Let r be the radius of circle and the each side of square is d1. 

2d1=2rd1=2r

Let the side of big square be d2. Again from the figure, the diameter of the circle is equal to side of big square. 

d2=2r

The side of small square is 2×r and the side of big square is 2r

(b) Let Q1 be the total charge of small square,  QC be the total charge of circle and Q2 be the total charge of large square. 

The surface charge density is same, the charge density is equal to ratio of charge and area 

Q1d12=QCπr2=Q2d22Q12r2=QCπr2=Q24r2Q12=QCπ=Q24

From this the value of Q1 is 

Q1=2QCπ

From this the value of Q2 is 

Q2=4QCπ

 

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