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Help needed in generalization

Hello everyone,

I don't know if the following generalization exists, but I want to give it a go. If you want to join, please do and help me. For this mini research to be a success, you need to help me with this problem. I found this to be little tricky and confusing stuff. Here it is.

Here is a regular pentagon named \(ABCDE\). Suppose, equal charges \(q\) are placed on each of its vertex.Now here's the calculation I need from your side. Find the magnitude of the net force exerted on a charge by the other \(4\) charges.

Details and Assumptions:

  • The length of each side of the pentagon is assumed to be \(a\).

  • Assume the medium to be vacuum.

Thanks \(!\)

Swapnil Das

Note by Swapnil Das
1 year, 7 months ago

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1 vote

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first find the distance between the test charge and 4 other charges. it is = a for 2 charge

first we find force due to them just write a vector and we find that one component of both is canceling

net ={2sin(36)kq^2}/(a^(2))

other which are at distance=2asin(54)

net due to them=(cos(18)/sin^2{54}){kq^2}/(2a^(2))

total={2sin(36)kq^2}/(a^(2))+(cos(18)/sin^2{54}){kq^2}/(2a^(2))

Aryan Goyat - 1 year, 7 months ago

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Nice!! There can be a shorter way, I suppose

Aakash Khandelwal - 1 year, 7 months ago

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