(a) An infinite sheet of conductor in x-y plane carries a uniform surface current K KR along x-direction. A Current carrying circular loop of radius R carrying a steady current / is placed above the sheet. Find the vector potential of the current carrying loop in the region s R by constructing appropriate Amperian loops.
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- Find the magnetic field H and current density J when the vector potential is given in the cylindrical coordinate system as follows.(b) A cylindrical wire (radius R) carries a current density flowing par- allel to the center axis and is uniformly distributed over the cross sectional area. What is the vector potential inside and outside the wire?Find the magnetic vector potential of a finite segment of straight wire, carrying current a current I.
- Given the scalar potential of line dipole, Φ=−μ⋅r /r^2, with μ=μex , find the corresponding complex potential and hence find the dipole’s stream function.An uncharged, infinitely long conducting cylinder of radius a is placed in an initially uniform clectric ficld E = Eoi, such that the cylinder's axis lics along the z axis. The resulting clectrostatic potential is V (x, y, z) = Vo for points inside the cylinder, and Ega?x x² + y? V (r, y, z) = Vo – Egx + for points outside the cylinder, where Vo is the (constant) clectrostatic potential on the conductor. Usc this expression to determine the resulting clectric ficld, E.Consider a spherical shell of inner and outer radius a and b, respectively, and conducting a uniform current density J = @J, (where Jo is al constant), which is always tangent to circles of constant latitude, as shown below. Find the vector potential A and the B field at the center of the sphere (i.e., at z=0).
- Repeat the preceding problem, with E=2xi+3x2k.(a) Verify that F is a solenoidal vector field. (b) Find a vector potential G .A spherical shell, of radius R, carrying a uniform surface charge σ, is set spinning atangular velocity ω. Find the magnetic field inside and outside the sphere from the vectorpotential
- Consider the velocity field, V = (x − 2y)i — (2x + y)j. What is the value of the velocity potential function at the point (2,3)?Investigate that the force field is below the constant and then obtain its potential functionProblem (1): If you have an infinite conductor wire with radius R carrying a current I, answer the following: a) Find its auxiliary field inside and outside the conductor? b) Find the volume current density inside and outside the conductor?