in this paper and in the nanotube studies, agreement is found.

The plan of the paper is as follows: In Sec. \[one\] the system to be studied is defined mathematically. In Sec. \[two\] its zero energy eigenstates are found when the electric field is zero, in which case there is no gap. In Sec. \[near\_zero\] the low energy description of the gapped state is developed. In Sec. \[four\] the topological theory of the anomalous Hall effect is briefly reviewed and then applied to the graphene system in order to calculate the quantized Hall conductivity. In Sec. \[five\] the anomalous Hall effect is considered again, this time without invoking the topological theory. In Sec. \[six\] an example is presented in order to illustrate the general results of the previous sections. Conclusions are presented in Sec. \[seven\].

Statement of the problem {#one}
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The inter-atomic distance between carbon atoms in graphene is approximately $1.42$Å. I consider a graphene sample in the presence of static electromagnetic fields $U$ and $\bm A$ that vary smoothly on this length scale. A long-wavelength description is therefore appropriate. This involves the Dirac Hamiltonian $$H=v\bm{\sigma}\cdot\left[-i\hbar\bm{\partial}_{\bm{r}}+e\bm{A(\bm{r})}\right]+U(\bm{r}).$$ where $\bm{\sigma}=(\sigma_x,\sigma_y)$ are standard Pauli matrices, $\bm{r}=(x,y)$, and $\bm{\partial}_{\bm{r}}=(\partial_x,\partial_y)$. Close to the charge 