A hollow, conducting sphere with an outer radius of 0.240 m and an inner radius of 0.200 m has a uniform surface charge density of + 6.67 * 10^-6 C/m^2. A charge of - 0.600 μC is now introduced into the cavity inside the sphere. Calculate the strength of the electric field at a distance 0.11 m from the center of the sphere.

Question

Israel Morrison

Physics

8 March, 03:24

A hollow, conducting sphere with an outer radius of 0.240 m and an inner radius of 0.200 m has a uniform surface charge density of + 6.67 * 10^-6 C/m^2. A charge of - 0.600 μC is now introduced into the cavity inside the sphere. Calculate the strength of the electric field at a distance 0.11 m from the center of the sphere.

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Seth Giles · Answer 1

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Explanation:

Gauss's law for electric field tells us that if the enclosed charge is zero the electric field is zero. Because we are 0.11 meters from the center of a hollow sphere the enclosed charge is zero. To further understand this concept let's take a look to the Gauss's law:

ФE = Q/eo

Where ФE is the electric flux, Q is the enclosed charge and eo is a constant. If the enclosed charge Q is zero we get that the electric flux is zero ФE = 0/eo = 0, and because the electric flux depends on the area, that is not zero, and the electric field, the only way the electric flux can be zero is if there is no electric field.