The figure below shows two nonconducting spherical shells fixed in place. Shell

Question

The figure below shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density +4.3 µC/m2 on its outer surface and radius 2.0 cm. The shell centers are separated by L = 14 cm. What are the magnitude and direction of the net electric field at x = 2.0 cm?

The figure below shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 mu C/m^2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density +4.3 mu C/m^2 on its outer surface and radius 2.0 cm. The shell centers are separated by L = 14 cm. What are the magnitude and direction of the net electric field at x = 2.0 cm?

Explanation / Answer

You can ignore shell 1 because at x = 2.0 cm you are inside that shell.

The charge on shell 2 is its area times its charge density:

4(.02 m)2(4.3 * 10-6 C/m2) = 2.16 * 10-8 C

Since we are given L = 14 cm, the distance from shell 2 to x is 12 cm. We need the field at that distance.

E = kq/r2 = (8.99 * 109 Nm2/C2)(2.16 * 10-8 C)/(0.12 m)2 = 1.35 * 104 N/C

which is the magnitude; the direction is the negativev x direction since the charge on shell 2 is positive.

Note that this means you might have to enter the magnitude as negative, depending upon your software:

-1.35 * 104 N/C

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