# Search results

1. ### I Current in an RL-Circuit

Why is initial current zero in an RL ciruit with an emf, but it is not in a charging RC circuit?
2. ### Relativity of Length

a) We use the definition of speed: v = delta_L/delta_t delta_t = delta_L/v = 45000 m/(0.99540*3*10^8 m/s) = 1.55*10^-4 s b) We use the length contraction equation: delta_L = L_0*sqrt(1-v^2/c^2) L_0 = delta_L/sqrt(1-v^2/c^2) = 45000 m/sqrt(1-0.99540^2) = 469698 m However, the solution shows...
3. ### Solving the Integral ∫dx/(1-x)

I solved the integral by two different methods and I get different answers. Method 1: ∫dx/(1-x) = -∫-dx/(1-x), u=1-x, du=-dx ∫dx/(1-x) = -∫du/u = -ln|u| = -ln|1-x| Method 2: ∫-dx/(x-1) = -∫dx/(x-1), u=x-1, du=dx ∫-dx/(x-1) = -∫du/u = -ln|u| = -ln|x-1| What am I doing wrong?
4. ### Convergence of a Power Series

We transform the series into a power series by a change of variable: y = √(x2+1) We have the following after substituting: ∑(2nyn/(3n+n3)) We use the ratio test: ρn = |(2n+1yn+1/(3n+1+(n+1)3)/(2nyn/(3n+n3)| = |(3n+n3)2y/(3n+1+(n+1)3)| ρ = |(3∞+∞3)2y/(3∞+1+(∞+1)3)| = |2y| |2y| < 1 |y| = 1/2...
5. ### Find the interval of convergence of this power series

∑((√(x2+1))n22/(3n+n3)) We use the ratio test: ρn = |2(3n+n3)√(x2+1)/(3n+1+(n+1)3)| ρ = |2√(x2+1)| ρ < 1 |2√(x2+1)| < 1 No "x" satisfies this expression, so I conclude the series doesn't converge for any "x". However the answer in the book says the series converges for |x| < √(5)/2. What am...
6. ### Find the Interval of Convergence of this Power Series: ∑(x^2n/(2^nn^2))

∑(x2n/(2nn2)) We use the ratio test: ρn = |(x2n2/(2(n+1)2)| ρ = |x2/2| ρ < 1 |x2| < 2 |x| = √(2) We investigate the endpoints: x = 2: ∑(4n/(2nn2) = ∑(2n/n2)) We use the preliminary test: limn→∞ 2n/n2 = ∞ Since the numerator is greater than the denominator. Therefore, x = 2 shouldn't be...
7. ### Infinite Series (The Ratio Test)

I found that ρn = √(2n+1)/(n+1). Then, I found ρ = lim when n→∞ |(1/n) (√(2n+1))/((1/n) (n+1))| = 0 Based on this result I concluded the series converges; however, the book answer says it diverges. What am I doing wrong?
8. ### Infinite Series (Integral Test)

After evaluating the integral I found the following: (1/3)tan-1(e∞/3) = (1/3)tan-1(∞) = (1/3)(nπ/2), where n is an odd number. In this case I found multiple solutions to the problem. How do you prove it converges?
9. ### Infinite Series (Integral Test)

I got the following expression: -(1/4)ln((n+2)/(n-2)) When I substitute "∞" in the expression I found it undefined. However, the book says the series converges. What am I doing wrong?
10. ### Limits of Sequences

If n is ∞, then ln (n) = ln (∞) = ∞ Then, 1/∞ = 0 Any number raised to "0" = 1, so the answer should be 1. However the book says the answer is e2. Could you provide me some help?
11. ### Path Followed by a Light Ray

This is an example from a textbook. They show the following: ∫nds = ∫r-2*ds = ∫r-2*√((dr)2+r2*(dθ)2) How do you obtain the expression for ds?
12. ### I How was F = ma obtained?

How was F = ma obtained? What is mass? If you say mass is amount of matter, then what is matter? How did they measure accelerations at that time?
13. ### Find the Euler Equation

∫(y'^2+y^2)dx Why I obtain two different equations? 1. y''=y 2. y'-xy+C=0
14. ### Derivation of the Optical Law of Reflection

Problem Statement: Derive the optical law of reflection. Hint: Let light go from the point A (x1, y1) to B (x2, y,2) via an arbitrary point P = (x, 0) on a mirror along the x axis. Set dt/dx = (n/c) dD/dx = 0, where D = distance APB, and show that then theta = phi. Relevant Equations: t = nD/c...
15. ### Studying Self-Studying Physics

I have a B.S. in Mechanical Enginerring and I am almost done with a PhD in Nanotechnology. Through these years I realized I really like physics and I would like to learn mmore advanced physics than the one I know so far. I would like to know how to study physics. My plan is to follow the...
16. ### How did Newton obtain F = ma?

Hi, I am concluding a phD in Nanotechnology and I just started studying physics by myself. I just wonder how did Newton obtain F = ma? What experiment did he perform? Which 2 variables did he measure? How did he measure them?
17. ### Computer Algebra System

I am stuying physics by myself and I would like to get a Computer Algebra System. Does anybody has any suggestions?
18. ### Engineering Relationship Mechanical Engineering and Nanotechnology

I got a B.S. in Mechanical Engineering and I am now doing a PhD in Nanotechnology in which I am synthesizing a nanomaterial. Someone just told me that nanotechnology is more like mechanical engineering and materials engineering than any other thing. Based on my work I can see the relationship...
19. ### TEM Images

What information do you get from TEM images and how do yo obtain it? I am analyzing hydroxyapatite (ceramic).
20. ### Teaching Physics with a PhD in Nanotechnology

I will get my PhD in Nanotechnology on June 2016 and I want to know if I can teach physics in college or at least in high school with this degree.
21. ### Engineering Difference Between Solid State Physicist and Materials Engineer

I would like to know what is the difference between a solid state physicist and a materials engineer. I mean, do they end up doing the same kind of job or research? If they both have the same purpose, how can they do it having different backgrounds? Which preparation is better for the purpose?
22. ### Second Phd

I´m now 30 years old (born in 1984) and I will be done with my Ph.d. in Nanotechnology in Mexico City. I am planning on getting married with my girlfriend (who is a U.S. citizen) on June 2016 and go live to the United States. I am now thinking what I would like to do after getting done with the...