Ecrit par ✅ Quiz : Bobine Et Solenoide
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
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{
"quiz_title": "Bobine Et Solenoide",
"quiz_slug": "01_bobine_et_solenoide_quiz",
"quiz_description": "Quiz Edu509 : Bobine Et Solenoide",
"quiz_settings": {
"time_limit": {
"time_value": 0,
"time_type": "minutes"
},
"hide_quiz_time_display": false,
"attempts_allowed": 0,
"passing_grade": 70,
"max_questions_for_answer": 0,
"questions_order": "rand",
"hide_question_number_overview": false,
"short_answer_characters_limit": 200
},
"questions": [
{
"question_order": 1,
"question_title": "Quel est le champ magnétique à l'intérieur d'un solénoïde de longueur \\\\( 0{,}4 \\\\mathrm{m} \\\\), comportant \\\\( 1200 \\\\) spires, parcouru par un courant de \\\\( 1{,}5 \\\\mathrm{A} \\\\) (air, \\\\( \\\\mu_0 = 4\\\\pi \\\\times 10^{-7} \\\\mathrm{T \\\\cdot m/A} \\\\)) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = \\\\frac{1200}{0{,}4} = 3000 \\\\mathrm{m}^{-1} \\\\). Le champ magnétique est \\\\( B = \\\\mu_0 n I = 4\\\\pi \\\\times 10^{-7} \\\\times 3000 \\\\times 1{,}5 = 1{,}2566 \\\\times 10^{-6} \\\\times 4500 = 5{,}6547 \\\\times 10^{-3} \\\\mathrm{T} \\\\), soit \\\\( 5{,}7 \\\\times 10^{-3} \\\\mathrm{T} \\\\) à deux chiffres significatifs.",
"answers": [
{
"answer_title": "\\\\( 5{,}7 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}8 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 7{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}3 \\\\times 10^{-2} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Une bobine de section \\\\( 2{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), longueur \\\\( 0{,}1 \\\\mathrm{m} \\\\), \\\\( 500 \\\\) spires, est parcourue par un courant qui passe de \\\\( 0 \\\\) à \\\\( 2{,}0 \\\\mathrm{A} \\\\) en \\\\( 0{,}05 \\\\mathrm{s} \\\\). Quelle est la tension d’auto-induction maximale (en valeur absolue) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 500/0{,}1 = 5000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (5000)^2 \\\\times 2{,}0 \\\\times 10^{-4} \\\\times 0{,}1 = 1{,}2566 \\\\times 10^{-6} \\\\times 25\\\\,000\\\\,000 \\\\times 2{,}0 \\\\times 10^{-4} \\\\times 0{,}1 = 0{,}0006283 \\\\mathrm{H} \\\\). \\\\( \\\\frac{dI}{dt} = 2{,}0/0{,}05 = 40 \\\\mathrm{A/s} \\\\). \\\\( e = L \\\\frac{dI}{dt} = 0{,}0006283 \\\\times 40 = 0{,}02513 \\\\mathrm{V} \\\\), soit \\\\( 2{,}5 \\\\times 10^{-2} \\\\mathrm{V} \\\\) à deux chiffres significatifs.",
"answers": [
{
"answer_title": "\\\\( 2{,}5 \\\\times 10^{-2} \\\\mathrm{V} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 4{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Quelle est l’inductance d’un solénoïde à air de \\\\( 0{,}5 \\\\mathrm{m} \\\\) de long, \\\\( 1000 \\\\) spires, section \\\\( 4{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1000/0{,}5 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (2000)^2 \\\\times 4{,}0 \\\\times 10^{-4} \\\\times 0{,}5 = 1{,}2566 \\\\times 10^{-6} \\\\times 4\\\\,000\\\\,000 \\\\times 4{,}0 \\\\times 10^{-4} \\\\times 0{,}5 = 2{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 4{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Un solénoïde de \\\\( 0{,}3 \\\\mathrm{m} \\\\), \\\\( 900 \\\\) spires, courant \\\\( 1{,}2 \\\\mathrm{A} \\\\), section \\\\( 5{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), air. Quelle est l’inductance ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 900/0{,}3 = 3000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (3000)^2 \\\\times 5{,}0 \\\\times 10^{-4} \\\\times 0{,}3 = 1{,}7 \\\\times 10^{-3} \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}7 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 4{,}5 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 9{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 3{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Un solénoïde à noyau de fer (\\\\( \\\\mu_r = 1500 \\\\)), longueur \\\\( 0{,}25 \\\\mathrm{m} \\\\), \\\\( 500 \\\\) spires, section \\\\( 8{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), courant \\\\( 0{,}60 \\\\mathrm{A} \\\\). Quel est le champ magnétique interne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 500/0{,}25 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( \\\\mu = 4\\\\pi \\\\times 10^{-7} \\\\times 1500 = 1{,}884 \\\\times 10^{-3} \\\\mathrm{T \\\\cdot m/A} \\\\). \\\\( B = \\\\mu n I = 1{,}884 \\\\times 10^{-3} \\\\times 2000 \\\\times 0{,}60 = 2{,}2608 \\\\mathrm{T} \\\\), soit \\\\( 1{,}9 \\\\mathrm{T} \\\\) à deux chiffres significatifs.",
"answers": [
{
"answer_title": "\\\\( 1{,}9 \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}57 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 5{,}7 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}057 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Quelle est l’énergie magnétique stockée dans une bobine d’inductance \\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\) parcourue par un courant de \\\\( 2{,}0 \\\\mathrm{A} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie magnétique est \\\\( E = \\\\frac{1}{2} L I^2 = 0{,}5 \\\\times 2{,}0 \\\\times 10^{-3} \\\\times (2{,}0)^2 = 0{,}5 \\\\times 2{,}0 \\\\times 10^{-3} \\\\times 4 = 4{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 4{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Pour un solénoïde à air de \\\\( 0{,}2 \\\\mathrm{m} \\\\), \\\\( 400 \\\\) spires, section \\\\( 3{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), courant passant de \\\\( 0 \\\\) à \\\\( 1{,}5 \\\\mathrm{A} \\\\) en \\\\( 0{,}10 \\\\mathrm{s} \\\\), quelle est la tension d’auto-induction maximale (en valeur absolue) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 400/0{,}2 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (2000)^2 \\\\times 3{,}0 \\\\times 10^{-4} \\\\times 0{,}2 = 3{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\). \\\\( \\\\frac{dI}{dt} = 1{,}5/0{,}10 = 15 \\\\mathrm{A/s} \\\\). \\\\( e = L \\\\frac{dI}{dt} = 3{,}0 \\\\times 10^{-4} \\\\times 15 = 4{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\).",
"answers": [
{
"answer_title": "\\\\( 4{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 3{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 9{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Un solénoïde à noyau de fer (\\\\( \\\\mu_r = 2000 \\\\)), longueur \\\\( 0{,}4 \\\\mathrm{m} \\\\), \\\\( 1600 \\\\) spires, section \\\\( 1{,}2 \\\\times 10^{-3} \\\\mathrm{m}^2 \\\\), courant \\\\( 0{,}80 \\\\mathrm{A} \\\\). Quelle est l’inductance ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1600/0{,}4 = 4000 \\\\mathrm{m}^{-1} \\\\). \\\\( \\\\mu = 4\\\\pi \\\\times 10^{-7} \\\\times 2000 = 2{,}5133 \\\\times 10^{-3} \\\\mathrm{T \\\\cdot m/A} \\\\). \\\\( L = \\\\mu n^2 S l = 2{,}5133 \\\\times 10^{-3} \\\\times (4000)^2 \\\\times 1{,}2 \\\\times 10^{-3} \\\\times 0{,}4 = 19{,}3 \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 19{,}3 \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 6{,}2 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 8{,}0 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}5 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Quelle est l’énergie magnétique stockée dans la bobine précédente (\\\\( L = 19{,}3 \\\\mathrm{H} \\\\), \\\\( I = 0{,}80 \\\\mathrm{A} \\\\)) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie magnétique est \\\\( E = \\\\frac{1}{2} L I^2 = 0{,}5 \\\\times 19{,}3 \\\\times (0{,}80)^2 = 0{,}5 \\\\times 19{,}3 \\\\times 0{,}64 = 6{,}2 \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 6{,}2 \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 15{,}4 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 9{,}7 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 3{,}1 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Pour un solénoïde de \\\\( 0{,}6 \\\\mathrm{m} \\\\), \\\\( 1800 \\\\) spires, courant \\\\( 2{,}0 \\\\mathrm{A} \\\\), air, quel est le champ magnétique interne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1800/0{,}6 = 3000 \\\\mathrm{m}^{-1} \\\\). \\\\( B = 4\\\\pi \\\\times 10^{-7} \\\\times 3000 \\\\times 2{,}0 = 1{,}2566 \\\\times 10^{-6} \\\\times 6000 = 7{,}5396 \\\\times 10^{-3} \\\\mathrm{T} \\\\), soit \\\\( 7{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\).",
"answers": [
{
"answer_title": "\\\\( 7{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 3{,}8 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}2 \\\\times 10^{-2} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Une bobine de \\\\( 0{,}2 \\\\mathrm{m} \\\\), \\\\( 400 \\\\) spires, section \\\\( 3{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), air. Quelle est son inductance ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 400/0{,}2 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (2000)^2 \\\\times 3{,}0 \\\\times 10^{-4} \\\\times 0{,}2 = 3{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 3{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}5 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 6{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 9{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Un solénoïde de \\\\( 0{,}5 \\\\mathrm{m} \\\\), \\\\( 1000 \\\\) spires, courant \\\\( 2{,}0 \\\\mathrm{A} \\\\), air. Quel est le champ magnétique interne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1000/0{,}5 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( B = 4\\\\pi \\\\times 10^{-7} \\\\times 2000 \\\\times 2{,}0 = 1{,}2566 \\\\times 10^{-6} \\\\times 4000 = 5{,}026 \\\\times 10^{-3} \\\\mathrm{T} \\\\), soit \\\\( 5{,}0 \\\\times 10^{-3} \\\\mathrm{T} \\\\).",
"answers": [
{
"answer_title": "\\\\( 5{,}0 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}0 \\\\times 10^{-2} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Une bobine d’inductance \\\\( 1{,}7 \\\\times 10^{-3} \\\\mathrm{H} \\\\) est parcourue par un courant de \\\\( 1{,}2 \\\\mathrm{A} \\\\). Quelle énergie magnétique est stockée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie magnétique est \\\\( E = \\\\frac{1}{2} L I^2 = 0{,}5 \\\\times 1{,}7 \\\\times 10^{-3} \\\\times (1{,}2)^2 = 0{,}5 \\\\times 1{,}7 \\\\times 10^{-3} \\\\times 1,44 = 1{,}224 \\\\times 10^{-3} \\\\mathrm{J} \\\\), soit \\\\( 1{,}2 \\\\times 10^{-3} \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}2 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}4 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-4} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Un solénoïde de \\\\( 0{,}3 \\\\mathrm{m} \\\\), \\\\( 900 \\\\) spires, courant \\\\( 1{,}2 \\\\mathrm{A} \\\\), air. Quel est le champ magnétique interne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 900/0{,}3 = 3000 \\\\mathrm{m}^{-1} \\\\). \\\\( B = 4\\\\pi \\\\times 10^{-7} \\\\times 3000 \\\\times 1{,}2 = 1{,}2566 \\\\times 10^{-6} \\\\times 3600 = 4{,}5238 \\\\times 10^{-3} \\\\mathrm{T} \\\\), soit \\\\( 4{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\).",
"answers": [
{
"answer_title": "\\\\( 4{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 9{,}0 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}2 \\\\times 10^{-2} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}5 \\\\times 10^{-3} \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Un solénoïde à noyau de fer (\\\\( \\\\mu_r = 2000 \\\\)), longueur \\\\( 0{,}4 \\\\mathrm{m} \\\\), \\\\( 1600 \\\\) spires, section \\\\( 1{,}2 \\\\times 10^{-3} \\\\mathrm{m}^2 \\\\), courant \\\\( 0{,}80 \\\\mathrm{A} \\\\). Quel est le champ magnétique interne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1600/0{,}4 = 4000 \\\\mathrm{m}^{-1} \\\\). \\\\( \\\\mu = 4\\\\pi \\\\times 10^{-7} \\\\times 2000 = 2{,}5133 \\\\times 10^{-3} \\\\mathrm{T \\\\cdot m/A} \\\\). \\\\( B = \\\\mu n I = 2{,}5133 \\\\times 10^{-3} \\\\times 4000 \\\\times 0{,}80 = 8{,}0426 \\\\mathrm{T} \\\\), soit \\\\( 8{,}0 \\\\mathrm{T} \\\\).",
"answers": [
{
"answer_title": "\\\\( 8{,}0 \\\\mathrm{T} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}5 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}2 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}8 \\\\mathrm{T} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Une bobine de \\\\( 0{,}25 \\\\mathrm{m} \\\\), \\\\( 500 \\\\) spires, section \\\\( 8{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), noyau de fer (\\\\( \\\\mu_r = 1500 \\\\)). Quelle est son inductance ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 500/0{,}25 = 2000 \\\\mathrm{m}^{-1} \\\\). \\\\( \\\\mu = 4\\\\pi \\\\times 10^{-7} \\\\times 1500 = 1{,}884 \\\\times 10^{-3} \\\\mathrm{T \\\\cdot m/A} \\\\). \\\\( L = \\\\mu n^2 S l = 1{,}884 \\\\times 10^{-3} \\\\times (2000)^2 \\\\times 8{,}0 \\\\times 10^{-4} \\\\times 0{,}25 = 1{,}9 \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}9 \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}19 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}019 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 19 \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Une bobine d’inductance \\\\( 1{,}9 \\\\mathrm{H} \\\\) est parcourue par un courant de \\\\( 0{,}60 \\\\mathrm{A} \\\\). Quelle énergie magnétique est stockée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie magnétique est \\\\( E = \\\\frac{1}{2} L I^2 = 0{,}5 \\\\times 1{,}9 \\\\times (0{,}60)^2 = 0{,}5 \\\\times 1{,}9 \\\\times 0,36 = 0{,}342 \\\\mathrm{J} \\\\), soit \\\\( 0{,}34 \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}34 \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}68 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}19 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}1 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Pour une bobine d’inductance \\\\( 3{,}0 \\\\times 10^{-4} \\\\mathrm{H} \\\\), si le courant varie de \\\\( 0 \\\\) à \\\\( 1{,}5 \\\\mathrm{A} \\\\) en \\\\( 0{,}10 \\\\mathrm{s} \\\\), quelle est la tension d’auto-induction maximale (en valeur absolue) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On utilise \\\\( e = L \\\\frac{dI}{dt} \\\\). \\\\( \\\\frac{dI}{dt} = 1{,}5/0{,}10 = 15 \\\\mathrm{A/s} \\\\). \\\\( e = 3{,}0 \\\\times 10^{-4} \\\\times 15 = 4{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\).",
"answers": [
{
"answer_title": "\\\\( 4{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}5 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 3{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 9{,}0 \\\\times 10^{-3} \\\\mathrm{V} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Un solénoïde de \\\\( 0{,}5 \\\\mathrm{m} \\\\), \\\\( 1000 \\\\) spires, courant \\\\( 2{,}0 \\\\mathrm{A} \\\\), section \\\\( 4{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\), air. Quelle est l’énergie magnétique stockée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On a déjà calculé \\\\( L = 2{,}0 \\\\times 10^{-3} \\\\mathrm{H} \\\\). \\\\( E = \\\\frac{1}{2} L I^2 = 0{,}5 \\\\times 2{,}0 \\\\times 10^{-3} \\\\times 4 = 4{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 4{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 8{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}0 \\\\times 10^{-3} \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un solénoïde de \\\\( 0{,}6 \\\\mathrm{m} \\\\), \\\\( 1800 \\\\) spires, courant \\\\( 2{,}0 \\\\mathrm{A} \\\\), air. Quelle est son inductance si la section est \\\\( 5{,}0 \\\\times 10^{-4} \\\\mathrm{m}^2 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\( n = 1800/0{,}6 = 3000 \\\\mathrm{m}^{-1} \\\\). \\\\( L = 4\\\\pi \\\\times 10^{-7} \\\\times (3000)^2 \\\\times 5{,}0 \\\\times 10^{-4} \\\\times 0{,}6 = 5{,}7 \\\\times 10^{-3} \\\\mathrm{H} \\\\).",
"answers": [
{
"answer_title": "\\\\( 5{,}7 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}2 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 2{,}5 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 7{,}5 \\\\times 10^{-3} \\\\mathrm{H} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
}
]
}