Ok, so then if I wanted to find the capacitance between a line charge and a cylindrical conducting shell around it, since I would have to define a potential difference, could I simply say the potential on the line is zero and the potential at the shell is the negative integral of the electric...
I know it seems a bit trivial, but what is the potential right at an infinite uniformly charged line?
Irregardless of reference point, the Potential will have a ln|s|, where s is the perpendicular distance to the line. Obviously this would result in infinity.
At the same time when I...
I am still not understanding. I completed the squares on \vec {C} \dotprod {\frac {d \vec {C}} {dt}} = 0 and get this really complex function that tells me nothing.
.5g^2[(t - \frac {3 V_0 sin \theta} {2g})^2 + (2 - \frac {9} {4} sin^2 \theta) \frac {V^2_0} {g^2}] = 0
The scalar...
Ok, so how does that help?
\sin \theta \cos \theta
is a function of maximum x-displacement.
The attached image shows the vector C that must never decrease in magnatude as the projectile moves along the arc.
Well, you got a function of theta only, but I'm not so sure this helps me. I am not trying to find an angle that will give me maximum range, but a maximum angle that will yield increasing distance from the origin.
I have nothing against that. I was just commenting how it is usually writen in books. Your way is a good middle step for if the question asks to write a vector from the info: a vector of length 5 units, 45 degs above the + x-axis... While the way I showed it is often a way a vector is presented.
"If you have some other vector which points along the 45 degree line (measured increasing counter-clockwise from the positive x-axis) and is five units long, its components are
(5 \cdot \cos 45^o, 5 \cdot \sin 45^o)
"
This is often also just writen as
[\sqrt{\frac{25}...
well, I just graphed it over and over using a calculator changing the angle until I got really really close to a non posative slope.
sin\theta \times cos\theta
has a maximum at 45 deg.
Position:
x = v_{0x}t = v cos(\theta)t
y = v_{0y}t -.5gt^2 = v sin(\theta)t - .5gt^2
Let...
I'm having trouble getting the answer without doing a guess and check.
Q: Find the maximum angle a projectile can be shot so that it's distance from the origin is always increasing. Air resistance negleced.
So there is the x and y position based on initial velocity, angle, and time, but I...
Thanks for the help guys. Yes, the commas were a dumb error and I should have noticed that.
So the triple sum was understood to go from one to three? I did not know that
\sum_{i,j,k}=\sum_{i=1}^{i=3}\sum_{j=1}^{j=3}\sum_{k=1}^{k=3 }
Hence me using the symbols i,j, and k for both a...
Vectors add just like integers. Add the x components and the y components. Draw yourself a picture for it to make more sense.
Once you have your Cx and Cy, you can use your choise of arctan, arcsin with corresponding sides to find the angle.
Difficulty with notation
I've always had trouble with notation, since there are so many ways to write the same thing.
This one is for Vector Analysis
First off, when speaking of unit vectos, such as i, j, k is it ok to use the notation;
{\hat i},{\hat j},{\hat k}
?
Such as in...