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Figure 1 depicts a long, uniformly charged, insulting cylinder surrounded by a long, uniformly charged insulating cylindrical shell. The two cylinders are concentric.

The radius of the inner cylinder is equal to $r_1 = 2.00$ cm. The inner radius of the cylindrical shell is equal to $r_2 = 4.40$ cm, and the outer radius of the cylindrical shell is equal to $r_3 = 6.20$ cm.

A surface charge density of $\sigma_1 = +4.60$ nC/cm$^2$ has been placed on the outer surface of the inner cylinder, and a surface charge density of $\sigma_2 = -3.80$ nC/cm$^2$ has been placed on the inner surface of the cylindrical shell, as shown in figure 1.

What is the electric field a distance $r_f = 5.20$ cm from the center of the inner cylinder?

A

$\vec{E} = 9.04 \times 10^5$ $\hat{r}$ N/C.

B

$\vec{E} = 3.25 \times 10^6$ $\hat{r}$ N/C.

C

$\vec{E} = -1.63 \times 10^6$ $\hat{r}$ N/C.

D

$\vec{E} = 2.77 \times 10^6$ $\hat{r}$ N/C.

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