33. a solid sphere of radius $40.0\text{ cm}$ has a total positive charge of $26.0\ \mu\text{c}$ uniformly distributed throughout its volume. calculate the magnitude of the electric field (a) $0\text{ cm}$, (b) $10.0\text{ cm}$, (c) $40.0\text{ cm}$, and (d) $60.0\text{ cm}$ from the center of the sphere.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Electrostatics", "Gausss Law" ], "new_concepts": [ "Electric Field of a Uniformly Charged Sphere" ], "current_concepts": [ "Electrostatics", "Gausss Law", "Electric Field of a Uniformly Charged Sphere" ] } ## Identify given parameters and formulas $$ \begin{aligned} &R = 0.400\text{ m},\quad Q = 26.0 \times 10^{-6}\text{ C},\quad k_e = 8.99 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2\ &E(r) = \frac{k_e Q r}{R^3} \quad \text{for } r \le R\ &E(r) = \frac{k_e Q}{r^2} \quad \text{for } r \ge R \end{aligned} $$ ## Calculate electric field inside the sphere $$ \begin{aligned} &\text{(a) } r = 0\text{ m}:\ &E(0) = 0\text{ N/C}\ \ &\text{(b) } r = 0.100\text{ m}:\ &E(0.100) = \frac{(8.99 \times 10^9)(26.0 \times 10^{-6})(0.100)}{(0.400)^3} = 3.65 \times 10^5\text{ N/C} \end{aligned} $$ ## Calculate electric field on and outside the sphere $$ \begin{aligned} &\text{(c) } r = 0.400\text{ m}:\ &E(0.400) = \frac{(8.99 \times 10^9)(26.0 \times 10^{-6})}{(0.400)^2} = 1.46 \times 10^6\text{ N/C}\ \ &\text{(d) } r = 0.600\text{ m}:\ &E(0.600) = \frac{(8.99 \times 10^9)(26.0 \times 10^{-6})}{(0.600)^2} = 6.49 \times 10^5\text{ N/C} \end{aligned} $$ (a) $0\text{ N/C}$ (b) $3.65 \times 10^5\text{ N/C}$ (c) $1.46 \times 10^6\text{ N/C}$ (d) $6.49 \times 10^5\text{ N/C}$ { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Gauss's Law for a Uniformly Charged Sphere" ] }

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Identify given parameters and formulas

Calculate electric field inside the sphere

Calculate electric field on and outside the sphere

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