A sphere of radius R = 0.295 m and uniform charge density 151 nC/m^3 lies at the center of a spherical, conducting shell of inner and outer radii 3.50R and 4.00R respectively. The conducting shell carries a total charge of Q = 66.7 nC. Determine the magnitude E(r) of the electric field at the given radial distances r from the center of the charge distribution: E(0.260R), E(3.90R), E(1.75R), E(7.30R)

To determine the electric field \( E(r) \) at different radial distances \( r \) from the center of a charge distribution that consists of a uniformly charged sphere and a conducting shell, we can apply **Gauss's Law**. Here’s how to approach it step by step:

### Parameters Given:
- Radius of sphere: \( R = 0.295 \, \text{m} \)
- Charge density of sphere: \( \rho = 151 \, \text{nC/m}^3 = 151 \times 10^{-9} \, \text{C/m}^3 \)
- Inner and outer radii of conducting shell: \( 3.50R \) and \( 4.00R \)
- Total charge on the conducting shell:

A sphere of radius R = 0.295 m and uniform charge density 151 nC/m^3 lies at the center of a spherical, conducting shell of inner and outer radii 3.50R and 4.00R respectively. The conducting shell carries a total charge of Q = 66.7 nC. Determine the magnitude E(r) of the electric field at the given radial distances r from the center of the charge distribution: E(0.260R), E(3.90R), E(1.75R), E(7.30R).

Solve an advanced electrostatics problem involving a sphere with uniform charge density and a surrounding conducting shell. Learn how to calculate the electric field at various distances using Gauss's Law, spherical symmetry, and superposition. This problem is suitable for university-level physics students.

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