Part A Consider a uniformly charged thin ring of radius R and charge Q . What is

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Part A

Consider a uniformly charged thin ring of radius R and charge Q . What is the charge density on the ring?

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Part B

A disc of radius R carries charge Q distributed uniformly on its surface. Find an expression for a differential charge element in the disc, in cylindrical polar coordinates. Use r as your radial coordinate and as your azimuthal coordinate.

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Part C

A disc of radius R caries charge density =ar2 , where a is a constant and  r is the distance between an arbitrary point on the disc and the disc's center. What is the total charge on the disc?

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Part D

Now consider a thin ring of radius R that carries charge density =0cos(/4) , where 0 is a constant. What is the total charge on the ring?

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Explanation / Answer

A)

charge density = total charge /length = Q/(2*pi*R)

B)

dq = elemental area*density

dq = 2*pi*r*dr*Q/(pi*R^2)

dq = (2*r*dr*Q)/R^2

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C)

small charge dq = 2*pi*r*dr*sigma*r^2

dq = sigma*2*pi*r^3*dr

Q = integration dq

Q = sigma*2*pi*r^4/4   from r=0 to r = R

Q = (1/2)*sigma*pi*R^2

(D)

dq = L*ds = Lo*cos(pi/4)*ds

Q = integration dq

Q = Lo*cos(pi/4)*2*pi*R

Q = 2*pi*R*Lo*cos(pi/4)

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