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...
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...
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...
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...
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...
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...
Homework Statement
Hey guys, I'm doing a problem on quadratic drag and energy dissipation. Basically, the question asks me to find the energy dissipated when a ball of mass 'm' is thrown directly upwards with a velocity 'v0', during the upwards journey to its maximum height, 'h'. The resistive...