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Electricity and Magnetism

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The Electric Field Between Two Charged Insulating Cylinders

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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.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

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.