1. Homework Statement
Show that ##\lim_{x \to a} f(x) = L## if and only if ##\lim_{x \to 0} f(x+a) = L##
2. Homework Equations

3. The Attempt at a Solution
For the forward direction (ie ##1 \Rightarrow 2##), I tried to first assume that 1. holds true (ie ##\forall \epsilon>0, \exists...
1. Homework Statement
Consider two circular, parallel, coaxial loops which are almost in contact. They are separated by 1.20mm, have 13.6cm as radius each. Both loops carry a current of I = 127A but in opposite directions. Find the magnetic force that the top loop exerts on the bottom loop...
Thanks, that's helpful. I understand that there are less waves in the vacuum medium, but how does this relate to the path length? Does the "extra number of wavelengths" mean path length? And as well, I still don't understand why having the glass would deflect the light rays in that way (both in...
1. Homework Statement
A double slit experiment is set up using a heliumneon laser (wavelength 633 nm). Suppose we add a small piece of glass (n = 1.50) over one of the slits. Then, the central point on the screen is occupied by what had been the m = 10 dark fringe. Determine the thickness t...
1. Homework Statement
Two laser beams, one of wavelength 633 nm and intensity I1 = 4.00x106 W/m2 with a circular beam profile D1 = 1.33 mm in diameter, and one of wavelength 442 nm and intensity I2 = 4.00x106 W/m2 with the same circular beam profile are fired, crossing at an angle of θ = 45°...
Thanks for everything thus far. Apparently there's been an error with the question grading, so I'm pretty sure our answer we have come up to is the correct one. Thanks for everything.
My bad again sorry. The computer system is telling me that I have made a mistake (I'm not sure where though). In the meantime, is my reasoning for the flux current correct? Thanks for your time and patience.
1. Homework Statement
Let d = 0.048m, L = 0.15m, r = 0.10m in the following diagram. Assume that the current I1 = 80.0A and I2 = 40.0A. Find the net force on the rectangle of wire and the direction it points, and state the direction of the emf if the current I1 is increasing in the direction...
It would be N = 1000 turns as we divide the total length by the spacing. I used this and i stilll get a wrong anser for a. (Using it as the total length of wire).
1. Homework Statement
A solenoid has length L = 2.0m, radius R = 28.0cm, field strength B = 2.7T. The field is maintained by superconducting wires, with cross section 2mm x 2mm, wound with a 2mm spacing between windings and 20 layers of winding. Use the result that the current is I = 215A.
a...
1. Homework Statement
A household appliance consumes 1800W of power from a 120V wall plug. Calculate the power consumed due to a wire of length L = 22.0m and diameter D1 = 1.628mm (with resistivity p = 1.680 x 108Ωm). If a house spends $1400 per year in electricity bills, how much money can...
1. Homework Statement
Consider a line of length L=0.950 m and uniform positive charge per unit length λ=2.9 μC. Point A is a distance x=0.23 m from the center of the line, while B is the same distance from the line but a distance y=0.28 m farther along the line; point C is a distance z=0.050 m...