Recent content by elements

$$\vec ρ = (3,4,5)$$ that would be my radius vector that I was using for the r, and what about the plane? Are we not looking for the field across the entire plane?

Yeah, it's just for sampling the points. My textbooks do it as well

Homework Statement A very thin, finite, and uniformly charged line of length 10 m carries a charge of 10 µC/m. Calculate the electric field intensity in a plane bisecting the line at ρ = 5 m. Homework EquationsThe Attempt at a Solution Not sure why I'm not getiting this but I've been at this...

examples such as: (a) ##\vec F = xy^2 \hat i + (x^2y+y) \hat j## Determine the total flux through a surface of a circle with radius 3. (b) If ##\vec D = (2 + 16 r^2) \vec{a_z}##, calculate ##\int \vec D \cdot \vec {dS}## over a hemispherical surface bounded by r = 2 and 0 ≤ θ ≤ π/2 (c) If...

Thank you, in general what's the best way to determine what to do, to use a theorem or direct evaluation? and how do you decide when to use gauss vs stokes vs greens

So the main thing I'm wondering is given a question how do we determine whether to use one of the fundamentals theorems of vector calculus or just directly evaluate the integral, and if usage of one of the theorems is required how do we determine which one to use in the situation? Examples are...

So since the parametrized path is ##\vec r(t) = t \hat i + t \hat j + 0 \hat k##, is the correct path to take then to evaluate the integral like so $$\int f(x,y,z) \vec {dl} = \int_0^1 f(x(t),y(t),z(t))(\vec {dx} \hat i + \vec {dy} \hat j +\vec {dz} \hat k)$$ $$= \int_0^1 (12t^2)x'(t)dt \hat i +...

I'm getting a bit confused by the specific notation in the question and am unsure what exactly it is asking here/how to proceed. Homework Statement Given a scalar function ##f## find (a) ##∫f \vec {dl}## and (b) ##∫fdl## along a straight line from ##(0, 0, 0)## to ##(1, 1, 0)##.Homework...

Ah ok I see so the actual bounds would be: Π/4 ≤ θ ≤ 3Π/4 0 ≤ Φ ≤ Π/4 Then the fact that |x| is a discontinous function doesn't actually matter in spherical coordinates at all?

it feels too simple but is it possible that the bounds would be: cos-1(-√2/2) ≤ ##\theta## ≤ cos-1(√2/2 and phi is bounded by 0 ≤ ##\phi##≤ cos-1(##\phi##=1/√2)

I do not have a picture of the volume but I tried to graph the it and I'm having trouble visualizing the integral because of the odd shape

Homework Statement This has been driving me crazy I can't for the life of me figure out how to convert the limits of this integral into spherical coordinates because there is an absolute value in the limits and I'm absolutely clueless as to what to do with with.Homework Equations $$\int_{\frac...

just the final volume of water displaced in the second eudiometer tube

Homework Statement When, using a eudiometer in a lab to collect gas over water, if you have to switch eudiometers is the final volume of water displaced equal to the water displaced in the first tube + the water displaced in the second, and would the pressure be calculated through the total...

Sorry forgot to give the picture