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True or False: In neutral materials, the atoms in the material tend to be randomly oriented which leads to a net zero magnetic field
True or False: When converting a magnetic field into its corresponding magnetic flux density in a material, the magnetic field if convolved with the free space permeability added to the material's relative permeability
True or False: When a magnetic field in one material passes into a different material, the tangential components of the magnetic field in both materials is equal
True or False: Given a loop with current flowing through it, the magnetic field generated by the loop can create inductance on the same loop independent of other current flowing loops
Given a loop of current defined with a radius of $r = 5m$ located at the origin and oriented normal to the $+z$ direction with a current of $\overline{I} = 275\mu A \hat{a}_{\theta}$ flowing through it, find the magnetic vector potential at $P = \left( -1,2,10 \right)$ is the space is defined with relative permeability of $\mu_r = 3.5$
Given a magnetic field of $\overline{H}_1 = 2y\hat{a}_x + 3xy\hat{a}_y - 10z\hat{a}_z $ in material 1, which is characterized by $\mu_r1 = 6$, find the magnetic field in material 2 when the previous field intersects with this region characterized with $\mu_r2 = 7.5$ and which generates a surface current of $\overline{J}_s = 5x\hat{a}_x - 2y\hat{a}_y$
Given a magnetic flux density of $\overline{B}_1 = \mu_0 \left( 2xy\hat{a}_x - 15z^2\hat{a}_y + \left( \frac{3}{x} + \frac{2}{y} \right)\hat{a}_z \right) $ in material 1, which is characterized by $\mu_{r1} = 1.5$, find the magnetic field in material 2 when the previous field intersects with this region characterized with $\mu_{r2} = 10$ and which generates a surface current of $\overline{J}_s = \left( x + y \right)\hat{a}_x + \left( x^2 + 2x + 1 \right)\hat{a}_y$
Given two loops of current which cause inductance on each other, find the magnitude of the current in loop 2 given $\mid I_1 \mid = 20mA$, $ L_{12} = 47pH $, $ L_{21} = 10\mu H $, and $ \Lambda_{12} = \Lambda_{21} $
Given a square loop present in a magnetic flux density and free to rotate along the y axis and centered at the origin, what is the torque applied by the flux density given as $\overline{B} = z^2 + 5z$ assuming that the loop has a width of $w = 5m$, the current traveling in the loop is $\mid I \mid = 25mA$, and the loop is currently parallel to the yz plane
Given $\overline{B} = \left( z^2 + 2z - 8 \right) e^{4t} \hat{a}_z$ in a cylindrical volume of radius $a = 20mm$, find the electric field inside of the volume due to this flux density at time $t = 0$