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Two thin spherical shells, one with radius R and the other with radius 2R, surround an isolated charge point particle. The ratio of the number of field lines through the larger sphere to the number through the smaller is

Question

Two thin spherical shells, one with radius R and the other with radius 2R, surround an isolated charge point particle. The ratio of the number of field lines through the larger sphere to the number through the smaller is

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Solution

The number of field lines through a sphere surrounding a charge is proportional to the magnitude of the charge inside the sphere. This is a consequence of Gauss's law, which states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space.

In this case, the charge enclosed by both spheres is the same, because they both surround the same isolated point charge. Therefore, the number of field lines through each sphere is the same.

So, the ratio of the number of field lines through the larger sphere to the number through the smaller sphere is 1:1.

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