// Numbas version: finer_feedback_settings
{"name": "Coulomb's Law for a pair of charges", "extensions": [], "custom_part_types": [], "resources": [["question-resources/CoulombForce1.png", "/srv/numbas/media/question-resources/CoulombForce1.png"], ["question-resources/CoulombForce2.png", "/srv/numbas/media/question-resources/CoulombForce2.png"], ["question-resources/CoulombForce3.png", "/srv/numbas/media/question-resources/CoulombForce3.png"], ["question-resources/CoulombForce4.png", "/srv/numbas/media/question-resources/CoulombForce4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Coulomb's Law for a pair of charges", "tags": ["coulomb", "elec", "field", "force", "mid1718"], "metadata": {"description": "Concepts and calculation involved in the use of Coulomb's Law for both the field and the force, including units and directions.", "licence": "All rights reserved"}, "statement": "<p>This question assesses understanding of the names and units of symbols in the Coulomb equation, the ability to perform calculation of quantities and to evaluate of force directions.&nbsp;&nbsp;</p>\n<p>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>The Coulomb field is for a point charge (the equation does not generally apply to all charge arrangements):</p>\n<table>\n<tbody>\n<tr>\n<td>Symbol</td>\n<td>Description</td>\n<td>Units</td>\n</tr>\n<tr>\n<td>$E$</td>\n<td>Electric field strength</td>\n<td>V/m (or N/C)</td>\n</tr>\n<tr>\n<td>$q$</td>\n<td>Point charge</td>\n<td>C</td>\n</tr>\n<tr>\n<td>$\\varepsilon_0$</td>\n<td>Permittivity of free space</td>\n<td>F/m</td>\n</tr>\n<tr>\n<td>$\\varepsilon_r$</td>\n<td>Relative permittivity of medium betweem the point charge and where the field is being established</td>\n<td>none</td>\n</tr>\n<tr>\n<td>$r$</td>\n<td>Distance from the point charge - it's definitely not a radius!</td>\n<td>m</td>\n</tr>\n<tr>\n<td>$\\hat{r}$</td>\n<td>This is the unit radial vector.&nbsp; It is not a displacement (which would have units of m).</td>\n<td>none</td>\n</tr>\n</tbody>\n</table>\n<p>In the calculation of the magnitude of the electric field strength, care has to be taken to correctly account for units.</p>\n<p>From the electric field, a force can be obtained using $F=qE$.&nbsp; For this problem the field has already been obtained, and all that's required is to multiply this by the magnitude of the second point charge.</p>\n<p>Since the charges are opposite in sign, they attract.</p>", "rulesets": {}, "extensions": [], "variables": {"q2": {"name": "q2", "group": "Ungrouped variables", "definition": "q2mu/10^6", "description": "<p>Second point charge in C.</p>", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "q1mu/10^6", "description": "<p>Point charge in C.</p>", "templateType": "anything"}, "efield": {"name": "efield", "group": "Ungrouped variables", "definition": "q1/(4 pi eps0 r^2)", "description": "<p>Electric field at the distant point in N/C.</p>", "templateType": "anything"}, "q2mu": {"name": "q2mu", "group": "Ungrouped variables", "definition": "random(1..20 except q1mu*10)*-0.1", "description": "<p>Charge on the second point charge in muC.</p>", "templateType": "anything"}, "rmm": {"name": "rmm", "group": "Ungrouped variables", "definition": "random(1..20)*0.1", "description": "<p>Radial distance from the point charge, mm.</p>", "templateType": "anything"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "rmm/1000", "description": "<p>Radial distance from the point charge, m.</p>", "templateType": "anything"}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "-efield*q2", "description": "<p>Magnitude of force on second point 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Coulomb's Law is embodied in the equation&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\vec{E}= {q\\over 4 \\pi \\varepsilon_0 \\varepsilon_r r^2}\\hat{r}$.</p>"}, {"type": "gapfill", "useCustomName": true, "customName": "Symbols, their meanings and their units", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: center;\">$\\vec{E}$ is&nbsp;[[0]] with units&nbsp;[[1]]</p>\n<p style=\"text-align: center;\">$q$ is&nbsp;[[2]] with units&nbsp;[[3]]</p>\n<p style=\"text-align: center;\">$\\varepsilon_0$ is&nbsp;[[4]] with units&nbsp;[[5]]</p>\n<p style=\"text-align: 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"marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the magnitude of the electric field {rmm}&nbsp;mm from a {q1mu}&nbsp;&mu;C point charge in vacuum.</p>\n<p style=\"text-align: center;\">$|\\vec{E}|=$ [[0]]&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "E value", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "efield*0.995", "maxValue": 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