# 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
2 years, 4 months ago

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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))

- 2 years, 4 months ago

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

- 2 years, 4 months ago