Final answer:
The question deals with finding magnetic fields around currents in different geometrical arrangements, a subject that pertains to college-level physics, specifically electromagnetism.
Step-by-step explanation:
The student is inquiring about magnetic fields generated by current-carrying conductors, which is a concept addressed in physics, specifically in the area of electromagnetism.
Using Ampère's Law and the Biot-Savart Law, one can determine the magnetic field generated by currents in various configurations such as loops and cylindrical wires.
For a loop on the xy-plane, the magnetic field at the center would be perpendicular to the plane of the loop.
Inside a cylindrical wire with radius R, uniform current density, and total current I, the magnetic field increases linearly with distance r from the center due to the proportion of current enclosed by Ampère's loop.
For points outside the wire, the magnetic field is found using the entire current I and follows an inverse relationship with distance.
The differential element of current, dI, can be calculated using the current density J and the differential area dA.
Your correct question is: Problem 4 (30 points) - For the following current distributions, sketch the distribution and find RdI and dI(RdI). (Remember dI has a weighting, spatial differential, and direction.) a) (1 point) Loop carrying current I on the xy plane with radius a centered at the origin. Give the answers in cylindrical coordinates. b) ( 2 points) Loop carrying current I parallel to the xy plane at a height of z=h with radius a centered at the origin. Give the answers in cylindrical coordinates. c) (6 points) Loop carrying current I on the xy plane with radius a centered at the point x= 2a,y=0. Give the answers in Cartesian coordinates. (Hint: use a parametric circle with 0≤t<2π ) d) (6 points) A plate conductor on the xy plane. Current is being injected at a rate of I into the center of the plate. The current spreads out evenly radially from the origin. (Hint: remember that the current crossing each concentric ring is also I. Calculate the surface current density first.) Give the answers in cylindrical coordinates. e) (6 points) A spherical shell of radius a[ m] is centered at the origin. The spherical shell is evenly charged with ρ . The shell is rotating around the z-axis with an angular velocity of ω . Give the answers in spherical coordinates. f) (3 points) A conducting ring defined in cylindrical coordinates by a≤ρ≤b,0≤ϕ< 2π,− with a total current I spread evenly throughout the conductor traveling counter-clockwise around the ring. Give the answers in cylindrical coordinates. g) (6 points) The spherical shell from part e) is now a solid sphere with radius a centered at the origin. The sphere is evenly charged with ρ and spinning about the z-axis with an angualar velocity of ω . Give the answers in spherical coordinates.