3. a uniformly charged ring of radius $10.0\text{ cm}$ has a total charge of $75.0\ \mu\text{c}$. find the electric field on the axis of the ring at (a) $1.00\text{ cm}$, (b) $5.00\text{ cm}$, (c) $30.0\text{ cm}$, and (d) $100\text{ cm}$ from the center of the ring.

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{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Electric Field of a Charged Ring", "Electrostatics" ], "current_concepts": [ "Electric Field of a Charged Ring", "Electrostatics" ] } ## Identify parameters and formula $$ \begin{aligned} &R = 10.0\text{ cm} = 0.100\text{ m} \ &Q = 75.0\ \mu\text{C} = 75.0 \times 10^{-6}\text{ C} \ &k_e = 8.99 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2 \ &E = \frac{k_e Q x}{(x^2 + R^2)^{3/2}} \end{aligned} $$ ## Calculate values for each distance $$ \begin{aligned} &\text{(a) } x = 0.0100\text{ m}: \ &E_a = \frac{(8.99 \times 10^9)(75.0 \times 10^{-6})(0.0100)}{(0.0100^2 + 0.100^2)^{3/2}} \approx 6.66 \times 10^6\text{ N/C} \ \ &\text{(b) } x = 0.0500\text{ m}: \ &E_b = \frac{(8.99 \times 10^9)(75.0 \times 10^{-6})(0.0500)}{(0.0500^2 + 0.100^2)^{3/2}} \approx 2.41 \times 10^7\text{ N/C} \ \ &\text{(c) } x = 0.300\text{ m}: \ &E_c = \frac{(8.99 \times 10^9)(75.0 \times 10^{-6})(0.300)}{(0.300^2 + 0.100^2)^{3/2}} \approx 6.39 \times 10^6\text{ N/C} \ \ &\text{(d) } x = 1.00\text{ m}: \ &E_d = \frac{(8.99 \times 10^9)(75.0 \times 10^{-6})(1.00)}{(1.00^2 + 0.100^2)^{3/2}} \approx 6.64 \times 10^5\text{ N/C} \end{aligned} $$ (a) $6.66 \times 10^6\text{ N/C}$ (b) $2.41 \times 10^7\text{ N/C}$ (c) $6.39 \times 10^6\text{ N/C}$ (d) $6.64 \times 10^5\text{ N/C}$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Electric Field of a Charged Ring" ] }

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Identify parameters and formula

Calculate values for each distance

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