How to solve for n in: A=((a)/(2R(n-1)^2)

Question

how to solve for n here

 

Answer 1

A = a/(2R(n-1)²)

 

(A/a)*2R = 1/(n-1)²

 

(n-1)² = a/(2AR)

n-1 = ±√(a/(2AR))

  n =  1 ± √(a/(2AR)),  2AR ≠ 0,  a ≠ 0  (if a=0 the original equation produces A=0, another way to look at it, n can not be 1)

 

This has two potential solutions.  Whether they are both valid or not depends on additional constraints on a/(2AR)  and n.  For example, if n must be real, then a/(2AR) > 0 is required.