2) Suppose a charge is placed at the center of two spheres. One sphere has a rad

Question

2) Suppose a charge is placed at the center of two spheres. One sphere has a radius R, and the other a radius 2R. The flux (D) of an electric field (E) surrounds the point charge Q. That same flux passes through the surface of the inner sphere and reaches the outer sphere How does the total flux passing through the inner sphere compare to the total flux passing through the outer sphere? How does the total charge enclosed by the inner sphere compare to the charge enclosed by the outer sphere? .How do the surface areas of the two spheres compare (be specific)? How does the flux per area of the two spheres compare (be specific)? . How does the electric field at the two spheres compare (be specific)? Using Gauss' Law, derive the formula for the electric field around a point charge.

Explanation / Answer

1]

Total flux passing through any closed surface = (charge enclosed)/Permittivity of the medium

So tottal flux passing through both spheres is same as charge enclosed by them both is same.

2]

Total charge enclose by two spheres is same.

3]

Surface area of a sphere = 4pir2

so, surface area of the outer sphere is 4 times that of the inner sphere.

4]

From part 1] and 3] we can see that flux per unit area of the outer sphere is 4 times smaller than that of the inner one.

5]

In this case, flux per unit area is the electric field so: E for inner sphere is 4 times the E at outer sphere.

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