*60.  mmh Two spherical shells have a common center. A -1.6 x 10-6 C charge is spread uniformly over the inner shell, which has a radius of 0.050 m. A +5.1 x 10-6 C charge is spread uniformly over the outer shell, which has a radius of 0.15 m. Find the magnitude and direction of the electric field at a distance (measured from the common center) of (a) 0.20 m, (b) 0.10 m, and (c) 0.025 m.

With the charges dispersed about the spherical surfaces, the Gaussian surfaces are also spheres.  So using Gauss’s law

Using  , and that the angle , we can find E from

 

 

So for (a) r = 0.20 m,

 

 

So with a net positive charge enclosed, the direction of the electric field will be radially outward from the outer shell.  The magnitude is found by plugging in below:

 

 

for (b) r = 0.10 m,

 

 

So with a net negative charge enclosed, the direction of the electric field will be radially inward to the inner shell.  The magnitude is found by plugging in below:

 

 

for (c) r = 0.025 m,

 

 

So with a net zero charge enclosed, there is no electric field, so there is no direction of the electric field.  The magnitude is found by plugging in below:

 

 

 

 

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This page last updated on June 6, 2018