Hi
A sphere with radius r is buried in an elastic ideal medium at pressure P1.
Inside the sphere I use energy E to create a variation of pressure of dP.
What variation dPx I would measure if the sphere was buried in a medium at pressure P2 using the same energy E?
Is it possible to solve...
##\iiint 3 dr d\rho d\phi##
The volume of a sphere is ##4\pi /3 r^3## so naturally the answer is ##4 \pi R^3##
But when I integrate I do:
##3 \iint r |_0^R d\rho d\phi##
##3R \int \rho |_0^{2\pi} d\phi##
##6R\pi * \phi |_0^\pi = 6R\pi^2##
What am I doing wrong?
I know that (a) is right, and (b) is wrong. The problem is with (c)... It seems correct to me! I can't see how this is not true. The electric charge o the sphere by itself will create an electric field, which will move the particle.
Back here again.. but I am sorry guys, only the parameters are on my paper so wouldn't be of much help to show. I basically have no clue on how to start solving this problem at all.
I stopped yesterday and let it sit overnight but still have no clue on how to approach the problem basically...
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I tried to solve it for some time and then looked at the solution manual, which got me completely lost. Those are the first lines of the solution :
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My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q
Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I...
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I am not very good at proofs. The only thing I have come up with is the following regularity. However, I am not sure how this can be related to the above problem.
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a) We know that ##Q_1=1,2\, \textrm{nC}## and ##Q_2=6\, \textrm{nC}##. By the TOTAL influence theorem:
$$-Q_1=Q_{2i}=-1,2\, \textrm{nC}$$
$$Q_2=Q_{2i}+Q_{2e}\rightarrow Q_{2e}=7,2\, \textrm{nC}$$
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$$V_A-V_\infty=$$
How was this potential difference thing...
Hi PF!
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Section 2.6 starts out with the problem of a "conducting sphere" near a point charge, but then it confusingly veers away to a problem where potential is prescribed to vary with azimuth and polar...
Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below?
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In a quantum mechanical exercise, I found the following Hamiltonian:
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Dear Forum,
My goal is to rotate several points on a sphere by a theta and phi. For example, I have a sphere where the elevation is theta (90 to -90) and the azimuthal is phi (-180 to 180). I have the following points on the sphere:
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This generate...
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$$I = \int{r^2dm}$$
$$dm = \sigma dV$$
$$dV = 4\pi r^2dr$$
$$\sigma = \frac{M}{\frac{4}{3}\pi*R^3}$$
$$I = \sigma 4 \pi \int_0^R{r^4 dr} = \frac{3*MR^2}{5},$$
which is not the correct moment of inertia of a sphere
I am currently reading Griffiths book for electrodynamics and having trouble making a jump in one of the problems. I have attached the problem (3.6) in question.
In the part that is highlighted, I don't see how we go from (1-cosθ) to (P0cosθ-P1cosθ)?
I can see that from the Legendre...
Picture :
My answer :
I guess net electric flux is 0.
so electric flux passing through surface 1 = -(electric flux passing through surface 2)
and electric flux passing through surface 1 is EA = E(pi)(r^2)
Is it correct? Thank you ...
I solved this problem on my own using the Energy formula. When I compared my answer to online answers (attached) as well as the griffiths solution manual, I noticed they also include the Electric field outside the sphere into their calculations. I did not and only use the Electric Field inside...
If I draw the fbd then some force will accelerate the car in horizontal direction which I think does not effect the string in vertical direction. So same tension regardless of acceleration.
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Hello,
I would like to ask one question. What is the equation for the lift force of a rotating sphere when flying through the air:
m = 0.25 g
v = 130 m/s
angular velocity = 105 rad/s
radius = 3 mm
air density = 1.2292 kg/m^3
air pressure = 101200 Pa
air temperature = 15 °C = 288.15 K
If anyone...
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A thin shell in reality doesn't have zero thickness. Consider the image below, showing a cross-section of a small portion of the shell:
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Gauss's Law...
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Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake.
I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...
I know I must have done something wrong somewhere here, but I cannot figure out exactly which one
Answer is supposed to be (2/5)MR2
Whatever disaster I have in the last image does not evaluate closely to that at all.
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Hello,
I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...
(A) incorrect, because opposite signs attract, and the sphere would've been drawn to the charged rod.
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