Recent content by azone

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    Find Total Magnetic Flux Through a Wire and Loop

    a) There is an infinitely long wire carrying a current I. There is a square loop with resistance R a distance a from the wire in the same plane. Find the total magnetic flux through the loop. b) There is an infinitely long wire carrying a current I in the z-direction. There is a square...
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    Time-dependent surface current density

    We have an infinitely long solenoid of radius R along the z-axis. The solenoid is electrically neutral. The surface current density K is dependent in time, K(t)=Kocos(wt) Find the magnetic field B(s,t) produced for s<R (inside solenoid), s>R (outside solenoid), and the associated electric...
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    Calculating Net Charge Using Electric Potential and Gauss' Law

    If we are given the formula for the electric potential V(r,theta) outside a spherical shell, how can we find the net charge on the shell? Essentially, I guess I'm a little confused about the relationship between Electric Potential and Net Charge. The way I thought about this is by finding...
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    How to Find Bound Charges in a Polarized Cylindrical Dielectric Shell?

    Homework Statement We have a long cylindrical, dielectric shell in the z-axis with inner radius R1 and outer radius R2. The polarization is given by P=k/s^2 (in cylindrical coordinates, it is only in the shat direction, i.e. no zhat or phihat) Homework Equations Find the bound surface...
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    Electric potential of cylinder problem

    Homework Statement A solid cylinder with radius R and length L has uniform charge density ro. Its base is in the x-y plane and it's axis is coincident with the z-axis (symmetrical about the z-axis) Homework Equations Find the electric potential at point P outside the cylinder at a...
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    How Do Eigenvectors of a Matrix Relate to Its Inverse?

    Suppose that B is the inverse of A. Show that if |psi> is an eigenvector of A with eigenvalue a not equal to 0, then |psi> is an eigenvector of B with eigenvalue 1/a. So I know that A|psi> = a|psi>, and I'm trying to prove that A^(-1)|psi> = 1/a|psi>. I tried simplifying A as a 2x2 matrix...
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    Expectations and Uncertainties of Lx^2 and Ly^2 in Eigenstate |l,m>

    Homework Statement Show that for the eigenstate |l,m> of L^2 and Lz, the expectation values of Lx^2 and Ly^2 are <Lx^2>=<Ly^2>=1/2*[l(l+1)-m^2]hbar^2 and for uncertainties, show that deltaLx=deltaLy={1/2*[l(l+1)-m^2]hbar^2}^(0.5) Homework Equations eigenvalues of L^2 are l(l+1)hbar^@...