To solve this problem, we will use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. 1. Inside the Sphere (r R, the sphere behaves as if all its charge were concentrated at its center. Therefore, the electric field is given by E = q / (4πε₀r²). To plot |E| as a function of distance r, you would have a graph with the following characteristics: - For r R, |E| decreases as 1/r². The plot would start at the origin (0,0), jump to q / (4πε₀R²) at r = R, and then decrease as 1/r² for r R. The plot would be discontinuous at r = R.

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To solve this problem, we will use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. 1. Inside the Sphere (r < R): For r < R, the sphere can be thought of as a superposition of an infinite number of infinitesimally thin spherical shells. The electric field due to each shell at a point inside the shell is zero. Therefore, the electric field at a point inside the sphere is zero. 2. On the Surface of the Sphere (r = R): At the surface of the sphere, the enclosed charge is q. According to Gauss's Law, the electric field is given by E = q / (4πε₀R²), where ε₀ is the permittivity of free space. 3. Outside the Sphere (r > R): For r > R, the sphere behaves as if all its charge were concentrated at its center. Therefore, the electric field is given by E = q / (4πε₀r²). To plot |E| as a function of distance r, you would have a graph with the following characteristics: - For r < R, |E| = 0. - At r = R, |E| jumps to q / (4πε₀R²). - For r > R, |E| decreases as 1/r². The plot would start at the origin (0,0), jump to q / (4πε₀R²) at r = R, and then decrease as 1/r² for r > R. The plot would be discontinuous at r = R.

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To solve this problem, we will use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. 1. Inside the Sphere (r < R): For r < R, the sphere can be thought of as a superposition of an infinite number of infinitesimally thin spherical shells. The electric field due to each shell at a point inside the shell is zero. Therefore, the electric field at a point inside the sphere is zero. 2. On the Surface of the Sphere (r = R): At the surface of the sphere, the enclosed charge is q. According to Gauss's Law, the electric field is given by E = q / (4πε₀R²), where ε₀ is the permittivity of free space. 3. Outside the Sphere (r > R): For r > R, the sphere behaves as if all its charge were concentrated at its center. Therefore, the electric field is given by E = q / (4πε₀r²). To plot |E| as a function of distance r, you would have a graph with the following characteristics: - For r < R, |E| = 0. - At r = R, |E| jumps to q / (4πε₀R²). - For r > R, |E| decreases as 1/r². The plot would start at the origin (0,0), jump to q / (4πε₀R²) at r = R, and then decrease as 1/r² for r > R. The plot would be discontinuous at r = R.

Find electric field inside and outside of uniformly charge sphere of radius R and q. Also, plot IEI asa function of distance r

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