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shefali sharma Grade: 12
        

a charge q is spread uniformly in form of line charge density q/3a on sides of equilateral triangle of side 3a. calculate potential at centroid .


an:2.634qk/a

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear shefali




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potential is a scalor quantity so potential due to whole triangle will be equal to 6 timen the potential due to portion BD


let a point P at a distance x from B


 dq = q/3a dx


PO =√(PD2 +DO2)


     =√(3a/2 -x)2 + (3a/2√3)2)


potenial due to charge dq at the center is


  dV= kdq/PO


  dV   =k q/3a dx/{√(3a/2 -x)2 + (3a/2√3)2}


  V = o3a/2 kq dx /3a{√(3a/2 -x)2 + (3a/2√3)2}


     =kq/3a  o3a/2  dx /{√(3a/2 -x)2 + (3a/2√3)2}


V = kq/3a [ log |x-3a/2  + {√(3a/2 -x)2 + (3a/2√3)2}|]  limit o to 3a/2


  =kq/3a [ log |3a/2 -3a/2  + {√(3a/2 -3a/2 )2 + (3a/2√3)2}|- log |0-3a/2  + {√(3a/2 -0)2 + (3a/2√3)2}|]


  = kq/3a [ log |(3a/2√3)|- log |-3a/2  + {√(3a/2 )2 + (3a/2√3)2}|]


  =-kq/3a log(2-√3)


total potential =6V =-2kq/a log(2-√3)


                           =2.63kq/a


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Badiuddin

7 years ago
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