(Solved): 3. (25 pts) Two identical small circular loop antennas of loop radius a are centered at the origin ...

3. (25 pts) Two identical small circular loop antennas of loop radius $a$ are centered at the origin as shown below. Loop 1 and Loop 2 have the loop areas in the $yz$ - and $xz$-planes, and carry constant currents $I_1$ and $I_2$ in the directions indicated, respectively. The two currents satisfy the relation $I_2=i{I}_1$. (a) (13 pts) In the far zone, find the expression for the total electric field $\mathbf{E}={\mathbf{E}}_1+{\mathbf{E}}_2$ in standard $(r,?,?)$ spherical coordinates. Use the given relation $I_2=j{I}_1$ so that the answer does not contain $I_2$. (b) (6 pts) Find the radiated power $P_{\text{rad }}$ as an expression containing $a$ and $I_1$. (c) (6 pts) Find the directivity $D(?,?)$ as a function of $?,?$.