Question
Asked Oct 22, 2019
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A wire having a uniform linear charge density λ is bent into the shape shown in the figure below. Find the electric potential at point O. (Use the following as necessary: Rke and λ.)

R
2R
2R
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R 2R 2R

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Expert Answer

Step 1

 Find the electric potential at the center O due to semicircular region as

The expression for the charge dQ present on the small element having length dS  is,

 

dQ Ads
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dQ Ads

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Step 2

Here λ is the line charge density

 

The length of arc subtended from the center is given by,

 

dS = λdθ

Substituting this expression for dS in the expression for dQ and write the expression for the electric potential at the center O due to the small segment of length as,

k,dQ
dV
R
kAds
R
kAds
R
- k,Ade
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k,dQ dV R kAds R kAds R - k,Ade

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Step 3

The expression for the total potential due to semi-circular section of wire at O is,

In...

av =kfade
0
VeIre =kA(T-0)
circ
kλπ
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av =kfade 0 VeIre =kA(T-0) circ kλπ

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