I tried it with no success..
I attempted to treat it like a ring of charge...finding E then integrating to find V.
Still no success.
I think I am getting lost in the "point any where on the axis inside or outside the tube".
any suggestions how to solve this?
Allow me to expand on what genneth started..
he is correct...E= - Del V
where del is the gradiate operator.
You have V in cartesian.
so del V = x(hat)*dV/dx+y(hat)*dV/dy+z(hat)*dV/dz
You text book should give the relationship for del V, don't forget the negative sign.
So take the...
Here is the question. a hollow, thin walled insulating cylinder of radius b and height h has charge Q uniformly distributed over its surface. Calculate the electric potential and field at all points along the z axis of the tube.
Outside the tube
Inside the tube.
I know how to find the...
Sort of
I think I see what is going on...I have to take the partial derivative of each value with respect to the cooresponding value, r to x theta to x and phi to x, then r, theta, and phi to y and then to z...this in turn will provide the conversion, right?
Is this essentially what how you...
Do I have to do this for y and z?
dT/dy= dT/dR*dR/dy+dT/d(theta)*d(theta)/dy+dT/d(phi)*d(phi)/dy
dT/dz= dT/dR*dR/dz+dT/d(theta)*d(theta)/dz+dT/d(phi)*d(phi)/dz
Then after this, its gets ugly, but I think this is how you do it...
x^=R^(cos...)+theta^(cos...)-phi^(sin phi)...
Correct so far?
First, thanks for responding...
Second, am I correct so far?
Third, I don't quite understand what you mean, could you expand on that?
Is it these values substitute into right hand side?
x=R sin theta cos phi
y=R sin theta sin phi
z=R cos theta
I am trying, but I...
I need to derive the expression for the gradient operator in spherical coordinates.
I know the following
R =sqrt(x^2+y^2+z^2)
theta, call it %, = arctan sqrt(x^2+y^2)/z
phi, arctan (y/x)
Using dT/dx= dT/dR*dr/dx+dT/d%*d%/dx+dT/dphi*dphi/dx, do partial derivates...
dR/dx =...
Got it...
I was making it harder than it was...
I solve for one of the variables, say a....
a=b+2c-d
Then I plug this value into L.
[b+2c-d, b,c,d]
I could set up in aug matrix, but I can pull the constants b, c, d right out to get the kernel basis.
Then my vectors are...
I think I have it...if there is constants for artibary numbers then those constants make up the kernal and the other is the range, correct?
SO if the the dim is 4 and the kernel is three, then the range is one...
if I solve it for a=b+2c-d, then the kernal is the constants, b, c, d times...
I need help. For this problem, you have to use the Gram-Schmidt process to make it orthogonal.
My trouble is finding the bais for the kernel of the linear map
L: R4 -> R1 defined by L([a,b,c,d)]=a-b-2c+d
I know the dimension of the kernel is 3, but how?
I have tried setting it...
Need some help finding the value of the input Resister...
Design a 7.5V zener regulator circuit using a 7.5 zener specified at 12 mA. The zener has an incremental resistance of 30 ohms and knee current of .5 mA. The regulator operates from a 10 V supply and has a 1.2 k-ohm load. What is the...
Need some help getting started...
Let T ={ [1, 0], [1, 1] }be a basis for R2 .
Given that Transition matrix P s←t
[ 2, 3 ; -1, 2],
find the basis S for R2.
Here is what I think...I started by letting v being any vector...
[1,0] and [0,1] and applied them to the transition...
I need some help to understand the concepts of span, basis, and dimension.
1-How do you determine if a set of vectors [in matrix form] span a region?
-Do you set the given matrix set to arbitary numbers and see if
there is a unique, infinite, or no solution?
ie, set a 4X4...
ok...think i get it
When I first did it, it didn't look right...almost too simple to be correct. Thanks for correcting me with my notation.
my text does have a format but this doesn't support the large brackets required for a 4X1 matrix.
I will try to make the matrix a little more easier...
still working with it...
if I set u=a1, b1, c1, d1 and v=a1, b1, c1, d1
set L(u+v)=(this is what I get)
[ (a1+a2)-(b1+b2)
0
(c1+c2)-(d1+d2)
0 ]
which equals L(u)+L(v)
for L(c*u)=c*L(u)
[c(a-b) c*0 c(c-d) c*0]
which converts to...
Alright...
I am still trying to figure out this message board...
I forgot to include what I already know...
I know you have to prove that L(u+v)=L(u)+ L(v) and L(c*u)=c*L(u), but I don't understand how to set it up.
I tried to separate it into a1 and a2, but just get confused...
Do I...
I need some help solving this...not even sure how to start...
Let L:R(4) goes to R(4) be the linear transformation defined by
-matlab notation, the value is a 4x1 column
L ( [ a b c d])=[ a-b
0
c-d
0 ]
Show...
New some help with some problems. I have tried them an listed what I have done so far...
1. A beam of electrons is sent along the x axis from - with kinetic energy E=7.5eV. The beam encounters a potential barrier of height V'=1eV and width 2a=1.2nm.
What fraction of the incident beam is...