# Recent content by yoghurt54

1. ### Heat loss through an insulated pipe

Homework Statement A pipe of radius R is maintained at temperature T. It is covered in insulation and the insulated pipe has radius r. Assume all surfaces lose heat through Newton's law of cooling \vec{J} = \vec{h} \Delta T, where the magnitude h is assumed to be constant. Show that...
2. ### Charged particle between two conducting plates

I've checked in on this after a day and I'm amazed and grateful at the responses I've gotten. First of all, I'd like to just say that if anyone has any issues with the question itself, I'm not the one who came up with it, nor the supposed value for the induced charge. I was merely stuck on...
3. ### Charged particle between two conducting plates

That's all she wrote boy! :-) Perhaps I should clarify that the plates are large, which I guess can mean that they can be considered tending to infinite area. Why is it "totally wrong"? Produce your own solution if you see the error.
4. ### Charged particle between two conducting plates

OK people, I've got it. The two plates are connected by a wire, so they are at equal potential. Note that as the plates are rectangular shaped, so are the equipotentials at each plate. We can call this potential zero. The charges induced are qL and qR. By the uniqueness theorem, the...
5. ### Charged particle between two conducting plates

The sheet of charge is mentioned in the question. Maybe the plates do not have even charge distributions, but the set-up can be simulated using the sheet charge as an image of the point charge?
6. ### Charged particle between two conducting plates

Homework Statement Two large conducting plates are separated by a distance 'L', and are connected together by a wire. A point charge 'q' is placed a distance 'x' from one of the plates. Show that the proportion of the charge induced on each plate is 'x/L' and '(L-x)/L'. (Hint: pretend the...
7. ### Show that A is an orthogonal matrix

Homework Statement If {aj} and {bj} are two separate sets of orthonormal basis sets, and are related by ai = \sumjnAijbj Show that A is an orthogonal matrix Homework Equations Provided above. The Attempt at a Solution Too much latex needed to show what I tried...
8. ### Charge placed between two plates

Homework Statement A sheet of charge +Q is in between two large plates of a capacitor. The plates are separated by a distance 'S', and are connected to each other by a wire. The sheet of charge is closer to one plate, at a distance 'a' from it. Show that the ratio to +Q of the charges...
9. ### Related to stokes theorem

Yeah you're right. I don't know why I got hung up on this, I guess I was reading too much into it.
10. ### Related to stokes theorem

Homework Statement \nabla \times f \vec{v} = f (\nabla \times \vec{v}) + ( \nabla f) \times \vec{v} Use with Stoke's theorem \oint _C \vec{A} . \vec{dr} = \int \int _S (\nabla \times \vec{A}) . \vec{dS} to show that \oint _c f \vec{dr} = \int \int _S \vec{dS} \times \nabla...
11. ### Vector fields

I'm not sure exactly what you mean, but my understanding of a vector field in this context is that it's a field in a coordinate system where each component is a function of the coordinates of that point, e.g. \vec{A}(x,y,z) = (x^2 - y^2, xz, y^3 + xz^2)
12. ### Vector fields

Hey - I'm stuck on a concept: Are ALL vector fields expressable as the product of a scalar field \varphi and a constant vector \vec{c}? i.e. Is there always a \varphi such that \vec{A} = \varphi \vec{c} ? for ANY field \vec{A}? I ask because there are some derivations from...
13. ### Dipole term in a quadrupole expansion

Alrightey then, thank you very much!
14. ### Dipole term in a quadrupole expansion

The two opposing dipoles - are they the pairings (above) -Q_1,Q_2 and Q_2, -Q_1 (below) ? Is this independent of what the actual magnitudes of the charges are, so long as the two like ones either side of the central one have the same magnitude?
15. ### Dipole term in a quadrupole expansion

Homework Statement There are three charges arranged on the z-axis. Charge +Q_2 at the origin, -Q_1 at (0,0,a) and -Q_1 at (0,0,-a). Using spherical polar coordinates (i.e the angle \vartheta is between r and the positive z-axis), find the potential at a point with a distance r from the...