\, 
\Big\{ 
g_A^2 \cL_{33}[m_\pi P_{\pi}(x,B^2), x B \hat{y},0]
\notag \\
&& \phantom{bigspacererer} + 
\frac{2}{9} g_{\D N}^2 
\cL_{33}[m_\pi P_{\pi}(x,B^2), x B \hat{y},\D]
\Big\}
\Bigg)
,\end{aligned}$$ where $F_2(B^2)$ is given in Eq. . The effects of the finite volume are encoded in the functions $
\cK_2(m,\bm{B},\D)$ and $\cL_{33}(m,\bm{B},\D)$, which are defined in the Appendix. In the limit that $B \to 0$, the result above accordingly vanishes: $B$ functions as a momentum transfer which is necessary for the magnetic form factor to be visible. Taking the derivative $$\lim_{B \to 0} 
\frac{2 M i}{B} 
\langle p(\bm{0}) \downarrow | J_3^+  | n(\bm{0}) \uparrow \rangle 
\notag
,$$ we can extract the magnetic moment $F_2(0)$ up to additive volume corrections. The corrections at $B = 0$ involving the $\cL_{33}(m_\pi, \bm{0}, \D)$ function are identical to the finite volume results in [@Beane:2004tw].[^7] Those results, however, were derived under the assumption that a momentum extrapolation to zero had been performed, or alternately that one had employed a background magnetic field. Devoid of these assumptions, the current insertion method produces a second finite volume correction to the magnetic moment involving $$\frac{ \partial \cK_2(m_\pi, B \hat{y}, \D)}{\partial B} \Big|_{B= 0} 
\notag
.$$

To investigate the effect of the finite volume on 