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True or False: Magnetic Flux density, $\overline{B}$, is a vector field which imbues the space it occupies with the ability to apply force to any charge
True or False: Magnetic fields can be caused by an electric current
True or False: Magnetic monopoles are the most basic type of magnetic field sources
True or False: The magnetic vector potential, $\overline{A}$, is defined as $\overline{B}=\nabla\times\overline{A}$
True or False: $\overline{H}$ and $\overline{B}$ are both representations of the magnetic field.
True or False: The Lorentz Force Law describes only the force of magnetic fields on a charged particle
Find the magnetic flux density at the center of a circular current loop with radius r, positioned in the x-y plane and symmetric about the z-axis, as shown below.
If an electric charge with charge $Q=1$ travels at velocity $\overline{U} = 1\hat{a}_x + 3\hat{a}_y+2\hat{a}_z$ in a region with electric field $\overline{E} =\frac{4}{3}x^2\hat{a}_x + 2xz\hat{a}_y+y^2\hat{a}_z $, and magnetic flux density $\overline{B}=x^2\hat{a}_x+y^2\hat{a}_y+z^2\hat{a}_z$, what is the force experienced by the charge?
Given a current $\overline{J}=J_\circ\frac{1}{zy}\hat{a}_x$ traveling along an infinitely thin wire along the x-axis in free space, find the differential vector potential at a the location given by $a=x\hat{a}_x+y\hat{a}_y+z\hat{a}_z$.
Given a sheet of current with current density $\overline{J} = b\hat{a}_x$, extending infinitely in both x and y and located at z=0, find the magnetic field in the region above the sheet.