Recent content by Vishakha

I got λ=1 if we leave the constants. But I don't understand why are we differentiating wrt λ?

λ+qλ = C ⇒dq = -(q+1)dλ/λ ... (1) dF/da = [(μa-a)2 { 2λq dq + q2 dλ} - 2q2λa (μ-1)2 ]/ 4πε0 (μa-a)2 = 0 After putting value of eq (1) I got final eq -q(q+1) dλ = 2λa

You mean I have to differentiate F wrt λ and distance between charges and q is constant.

You are right. F shouldn't be zero but I don't find any mistake in my calculation.

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

I already wrote that in The attempt at a solution section. F= λq2/4πε0 (μa-a)2 ⇒ dF/dq = 2λq/4πε0(μa-a)2 =0 ⇒ 2λq = 0 q≠0 ⇒λ=0

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...

$$\lim_{x \to 0} \frac {e^x-1}{x }$$ is a special case of $$\lim_{x \to 0} \frac {a^x-1}{x }$$

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.

It gives me expansion of cosine series. I think for final answer may be I have to put value of π. Thanks 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