(Solved): [25 points] The figure shows a bar magnet of magnetic dipole moment =2 A. m2 and a partial loop c ...

[25 points] The figure shows a bar magnet of magnetic dipole moment $?=2$ A. ${\mathrm{m}}^2$ and a partial loop circuit of radius $\mathrm{R}=6\mathrm{cm}$ and carrying a current $\mathrm{I}=6\mathrm{A}$. Point $O$ is the center of the partial loop. The bar magnet is at a distance $r=0.12\mathrm{m}$ from point $O$. a) [6 points] Find the magnitude of magnetic field due to the loop at the center of the loop. ${\vec{B}}_{\text{loop }}=$ b) [4 points] Write the expression of magnetic field vector due to the loop at the center of the loop. ${\vec{B}}_{\text{loop }}=<$ $>[\mathrm{T}]$ c) [6 points] Find the magnitude of magnetic field due to the magnet at the center of the loop. ${\vec{B}}_{\text{magnet }}=$ [T] d) [4 points] Write the expression of magnetic field vector due to the magnet at the center of the loop. ${\vec{B}}_{\text{magnet }}=<$ [T] e) [5 points] Write the expression of net magnetic field vector at the center of the loop.