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

#ElectricityAndMagnetism

Easy Math Editor

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Comments

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 - 5 years, 1 month ago

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

Aakash Khandelwal - 5 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$