If I used q+λq = C ⇒ λq=C-q
Then 2λq=0 ⇒ 2(C-q) = 0 ⇒q=C
Let F is function of distance
F = λq2/4πε0a2(μ-1)2
⇒ -2λq2/4πε0a3(μ-1)2 = 0
⇒ -2λq2 = 0
⇒ λq= 0 or λq=C
Homework Statement
Two point charges q and λq located at the points, x=a & x=μa respectively. If the sum of the two charges is constant,what is the value of λ for which the magnitude of the electrostatic force is maximum?Homework Equations
The Attempt at a Solution
For force to be maximum dF/dq...
By M is not scalar multiple of cos(π M/6) I meant cos(π M/6) ≠ M cos(π/6).
I was calculating cos(A)=cos(PDP-1) but instead of ##f(A) = P f(D) P^{-1}## I was doing ##f(A) = f(PDP^{-1})##.Thanks for pointing that out.
Thank you for help.
Of course it isn't !
I found similar problem like this in which we have to find cos(A) where A=(π/2) \begin{pmatrix}
1 & 1 \\
1 & 1 \\
\end{pmatrix}. The process is they first find eigen vectors and then used diagonalization formula.
cos(A)= PDP-1
I'm not sure it is D or cos(D).
Homework Statement
Given a matrix M={{2,1},{1,2}} then value of cos( (π*M)/6 )Homework EquationsThe Attempt at a Solution
Eigen values are π/6 and π/2 and eigen vectors are (π/6,{-1,1}) and (π/2,{1,1}).
Diagonalize matrix is {{π/6,0},{0,π/2}}
I got same value (√3/2)M