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  1. J

    Calculate the electric potential and field

    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...
  2. J

    Derive expression for gradient operator in spherical coordinates

    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 =...
  3. J

    Find basis for the kernel of linear map

    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...
  4. J

    Zener diode-finding Resistor value

    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...
  5. J

    Linear Transformation

    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...
  6. J

    Span, Basis, Dimension

    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...
  7. J

    Linear algebra

    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...
  8. J

    Potential barriers, etc.

    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...
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