A conducting loop carries a steady, counterclockwise current I. The loop consists of two half-circles connected by vertical, equal-length straight sections, forming a horizontal loop. The radius of the right half-circle is R_A (smaller radius) and the radius of the left half-circle is R_B (larger radius).
(i) Find the magnitude and direction of the magnetic field at the center point P of the loop. (ii) Calculate the magnetic dipole moment of the loop.

• A. $\(\begin{array}{l}\]\text{i. }\) B_{\(\text\) {Total }}=\(\frac{\mu_{0}\) I}{4}\(\left\)(\(\frac{1}{R_{A}\)}+\(\frac{1}{R_{B}\)}\(\right\)) \(\text{, out of the page;}\)\\ \(\text{ii. }\) \(\mu\)=\(\frac{\pi I}{2}\[\left\)(R_{A}^{2}+R_{B}^{2}\(\right\)) \(\text{, out of the page}\]\end{array}\)$
• B. $\(\begin{array}{l}\]\text{i. }\)B_{\(\text{Total }\)}=\(\frac{\mu_0I}{4}\[\left\)(\(\frac{1}{R_{A}\)}+\(\frac{1}{R_{B}\)}\(\right\))\(\text{, out of the page;}\)\\ \(\text{ii. }\]\mu\)=\(\pi\) I\ \(\left\)(R_{A}^2+R_{B}^2\(\right\))\(\text{, into the page}\).\(\end{array}\)$
• C. $\(\begin{array}{l}\]\text{i. }\)B_{\(\text{Total }\)}=\(\mu\) _0I\(\left\)(\(\frac{1}{R_A}\)+\(\frac{1}{R_B}\[\right\))\(\text{, out of the page;}\)\\ \(\text{ii. }\]\mu\) =\(\frac{\pi I}{2}\)\ \(\left\)(R_A^2+R_B^2\(\right\))\(\text{, into the page}\).\(\end{array}\)$
• D. $\(\begin{array}{l}\]\text{i. }\)B_{\(\text{Total }\)}=\(\mu\) _0I\(\left\)(\(\frac{1}{R_A}\)+\(\frac{1}{R_B}\[\right\))\(\text{, out of the page;}\)\\ \(\text{ii. }\]\mu\) =\(\pi\) I\ \(\left\)(R_A^2+R_B^2\(\right\))\(\text{, out of the page}\).\(\end{array}\)$