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A charge Q is spread uniformly in the form of a line charge density =Q/3a on the sides of an equilateral triangle of perimeter 3a. Calculate the potential at centroid C of the triangle. reply....

A charge Q is spread uniformly in the form of a line charge density  =Q/3a on the sides of an equilateral triangle of perimeter 3a. Calculate the potential at centroid C of the triangle. reply....

Grade:Upto college level

1 Answers

Rahul askIITiansExpert.IITR
110 Points
10 years ago
its a fairly simple question

see if you calculate the potential by a side multiply it by 3 and u will get the answer.

now consider a problem with a line of unform charge(linear charge density:

find the distance between each side and the centroid by first using pythagoras theoram and then the property of centroid which says that it divides a median in a ratio of 1:2, relative to the point.

let this distance be a

now just concentrate between the centroid and the side

drop a perpendicular from centroid to the side (it will intersect exaclty at the centre of the side since medians in a equilateral tringle are same as altitudes)

take an arbitrary element dx at the side with a distnce of x from the intersection point A

find the expresion of potetial at centroid due to that small element using the potential expression

kq/x, where x should be sq rt(x^2 + d^2), d being the length of perpendicular

integrate and the answer follows.........

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