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Electricity and Magnetism

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Moderate

The Electric Field Outside Two Charged Conducting Cylinders

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Figure 1 depicts a long, charged, conducting cylinder, surrounded by a long, charged conducting 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 inner cylinder. Sufficient charge has been added to the outer cylindrical shell so that the electric field at a radius of $r_f = r_3 = 6.20$ cm is equal to $\vec{E}(r_f) = -2.10 \times 10^6 \text{ } \hat{r}$ N/C.