A charged particle is held at the center of two concentric conducting spherical shells. Figure (a) shows a cross section. Figure (b) gives the net flux through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by 5 = 5.0 x 105 N-m²/C. What are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell B? B (5/ N 01) (b)

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**Title: Understanding Electric Flux and Charge Distribution in Concentric Conducting Spherical Shells**

**Introduction:**
A charged particle is held at the center of two concentric conducting spherical shells. This concept is critical in understanding various principles of electrostatics, particularly Gauss's Law and charge distribution. The following discussion will examine the charge distribution through graphical analysis.

**Figures Explanation:**

**Figure (a): Cross Section of Concentric Spherical Shells**
   - This diagram illustrates two concentric spherical shells labeled as Shell A (inner shell) and Shell B (outer shell).
   - Each shell is conductive and spherical, with a centrally placed charged particle within these shells.
   - The shells are centered on the charging particle.

**Figure (b): Net Electric Flux (Φ)**
   - This graph depicts the net electric flux Φ through a Gaussian sphere centered on the particle as a function of the radius r of the sphere.
   - The vertical axis shows Φ in increments of \(Φ_s = 5.0 \times 10^5 \text{ N·m}^2/\text{C}\).
   - The horizontal axis represents the radius \(r\) of the Gaussian sphere.
   - The graph steps through different flux values as the radius changes, indicating the presence of charges at specific points.

**Graph Analysis:**
   - At the center (r = 0), the net flux is zero.
   - Moving outward, the flux increases linearly reaching \(Φ_s\) at a certain radius, suggesting the presence of a positive charge within the inner shell.
   - As the radius increases further to encompass Shell A, the flux steps down to zero again, indicating that Shell A holds a net charge that offsets the central positive charge.
   - Continuing outward, the flux steps down to \(-Φ_s\), suggesting the presence of a negative charge.
   - Finally, the flux returns to zero as the radius fully encompasses Shell B, indicating that Shell B must possess a net charge neutralizing the observed \(-Φ_s\).

**Questions:**

(a) **Charge of the Central Particle:**
   - The central particle has a charge that produces a net flux of \(Φ_s = 5.0 \times 10^5 \text{ N·m}^2/\text{C}\).

(b) **Net Charge of Shell A:**
   - Shell A offsets the flux created by the central particle, implying that
Transcribed Image Text:**Title: Understanding Electric Flux and Charge Distribution in Concentric Conducting Spherical Shells** **Introduction:** A charged particle is held at the center of two concentric conducting spherical shells. This concept is critical in understanding various principles of electrostatics, particularly Gauss's Law and charge distribution. The following discussion will examine the charge distribution through graphical analysis. **Figures Explanation:** **Figure (a): Cross Section of Concentric Spherical Shells** - This diagram illustrates two concentric spherical shells labeled as Shell A (inner shell) and Shell B (outer shell). - Each shell is conductive and spherical, with a centrally placed charged particle within these shells. - The shells are centered on the charging particle. **Figure (b): Net Electric Flux (Φ)** - This graph depicts the net electric flux Φ through a Gaussian sphere centered on the particle as a function of the radius r of the sphere. - The vertical axis shows Φ in increments of \(Φ_s = 5.0 \times 10^5 \text{ N·m}^2/\text{C}\). - The horizontal axis represents the radius \(r\) of the Gaussian sphere. - The graph steps through different flux values as the radius changes, indicating the presence of charges at specific points. **Graph Analysis:** - At the center (r = 0), the net flux is zero. - Moving outward, the flux increases linearly reaching \(Φ_s\) at a certain radius, suggesting the presence of a positive charge within the inner shell. - As the radius increases further to encompass Shell A, the flux steps down to zero again, indicating that Shell A holds a net charge that offsets the central positive charge. - Continuing outward, the flux steps down to \(-Φ_s\), suggesting the presence of a negative charge. - Finally, the flux returns to zero as the radius fully encompasses Shell B, indicating that Shell B must possess a net charge neutralizing the observed \(-Φ_s\). **Questions:** (a) **Charge of the Central Particle:** - The central particle has a charge that produces a net flux of \(Φ_s = 5.0 \times 10^5 \text{ N·m}^2/\text{C}\). (b) **Net Charge of Shell A:** - Shell A offsets the flux created by the central particle, implying that
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