E n q ΔS r q dS q q 半径に寄らない! これを円錐部分について見てみる

㸯㸲 ࢞࢘ࢫࡢἲ๎
㸦ド᫂㸧㹑ࡀ⌫㠃ࡢ࡜ࡁ㸹
E (r )
E (r )࣭n (r ) 㸻㹃n(r )
Ⅼ㟁Ⲵࡢሙྜ㸸
r
O
Ⅼ㟁Ⲵ㹯ࡀ࠶ࡿ࡜ࡁ㸪௵ពࡢ㛢᭤㠃㹑࡟ࡘ࠸࡚㸪
GS
㸻_E (r )_
n (r )ࢆ㛢᭤㠃ࡢእྥࡁ༢఩ἲ⥺࣋ࢡࢺࣝ࡜ࡋ࡚㸪
㹐 㹯
S
E (r )࣭n (r ) G㹑㸻㹃n(r ) G㹑 T
㸻࣭̿̿̿̿̿̿㸦୍ᐃ㸧
㹐2
4ȧH0
㹯
̿̿
㸻H0
㸦㹯ࡀ㹑ࡢ୰㸧
㹹
㸮 㸦㹯ࡀ㹑ࡢእ㸧
n
㹃
q
T
Қ 㹃n(r )GS 㸻̿̿̿̿̿ GS
4ȧH0 㹐2
T
㸻̿̿̿̿̿ 4ȧ㹐2
4ȧH0 㹐2
T
㸻̿̿
H0
ǼS
r
༙ᚄ࡟ᐤࡽ࡞࠸㸟
ࡇࢀࢆ෇㗹㒊ศ࡟ࡘ࠸࡚ぢ࡚ࡳࡿ
O
෇㗹㒊ศ࡟ࡘ࠸࡚㸹
Ⅼ㟁Ⲵࡀ㹑ࡢ୰࡟࠶ࡿ୍⯡ࡢሙྜ㸹
㸦ド᫂㸧
n
㹃a(r )
㹃
ȟ
㹃(r )
㹐
ǼS
ǼS
㹃a
ǼS’
ǼD
ǼD
㹯 U
㹯
㹑
ǼS㹐2
̿̿ 㸻̿̿
ǼD
U2 ǼS 㹃a
̿̿ 㸻̿̿
㹃U2 ǼD
㹃
̿̿ 㸻̿̿
㹃a
㹐2
㸿
Ǽࡀ༑ศᑠࡉ࠸࡜ࡁ
㹃࣭n Ǽ㹑㸻㹃FRVȟǼ㹑
㸻㹃Ǽ㹑’
Қ㹃ǼS㸻㹃aǼD
㸻㹃aǼD
T
㹃࣭n G㹑㸻 㹃a GD㸻̿̿
Ȝ0
Ⅼ㟁Ⲵ㹯ࢆᅖࡴ௵ពࡢ㛢᭤㠃㹑࡟ࡘ࠸࡚㸪
T
㹃(r )࣭n (r ) G㹑㸻̿̿
Ȝ0
n T1
Ⅼ㟁Ⲵࡀ㹑ࡢእ࡟࠶ࡿሙྜ㸹
㸦ド᫂㸧
Ⅼ㟁Ⲵࡀከᩘ࠶ࡿሙྜ㸹
㹬ಶࡢⅬ㟁Ⲵ㸹㹯1㹯2͐㹯n
ࡑࢀࡒࢀࡀసࡿ㟁ሙ㸹㹃1(r )㹃2(r )͐㹃n(r )
㹃1
㹃2
ǼS1
T2
㹃㸻Ȋ㹃i
n
ǼS2
㹃࣭n G㹑㸻Ȋ 㹃i࣭n G㹑
㹑
ǼD
ྑ㎶ࡢྛ㡯࡟ࡘ࠸࡚
㸿
㹯i
̿̿ 㸦㹯i ࡀ㹑ࡢ୰㸧
㹃i࣭n G㹑㸻Ȝ0
㸮 㸦㹯i ࡀ㹑ࡢእ㸧
㹃1nǼS1㸻㹃aǼa
䡗
T1㸺S/2 㸪 T2㸼S/2 э 㹃1࣭n1 ࡜㹃2࣭n 2 ࡢ➢ྕ
ࡣ㏫
Қ㹃2nǼS 2㸻㸫㹃aǼa
㹃(r )࣭n(r ) G㹑㸻̿̿Ȋ㹯i Ȝ0
᭤㠃㹑そ࠺௚ࡢࡍ࡭࡚ࡢ෇㗹࡟ࡘ࠸࡚ྠᵝ
㻌
䡚㻌 㻔㻠㻚㻝㻝㻕
Қ 㹃(r )࣭n (r ) G㹑㸻㸮 ࢞࢘ࢫࡢἲ๎ࡢᛂ⏝
౛㢟㸰㸸 ౛㢟㸯࡛ồࡵࡓ㸪┤⥺ୖ࡟୍ᵝ࡟ศᕸࡍࡿ㟁Ⲵ
࡟ࡼࡿ㟁ሙࢆ㸪࢞࢘ࢫࡢἲ๎࡟ࡼࡗ࡚ồࡵࡼ㸬
㹙␎ゎ㹛
㟁Ⲵศᕸࡢᑐ⛠ᛶࡣ㸪
㸯㸬ᅇ㌿ᑐ⛠
㸰㸬୪㐍ᑐ⛠
㸱㸬㸰ᅇᑐ⛠
㹑
㟁ሙࡣ㸪
㸯㸬┤⥺࡟ᆶ┤࡛ᨺᑕ≧
㸰㸬┤⥺࠿ࡽࡢ㊥㞳ࡢࡳ࡟౫Ꮡ
┤⥺ࢆ୰ᚰ㍈࡜ࡍࡿ෇⟄≧ࡢ㛢᭤㠃㹑࡟࢞࢘ࢫࡢἲ๎
ࢆ㐺⏝ࡍࡿ㸬
ୖୗ㠃㸸㹃n㸻㸮
ഃ㠃 㸸㹃n㸻_㹃_㸻㹃
౛㢟㸱 ༙ᚄ㹟ࡢ⌫ෆ࡟㟁Ⲵ㹏ࡀ୍ᵝ࡟ศᕸࡋ࡚࠸ࡿ࡜
ࡁ
㟁Ⲵศᕸࡢᑐ⛠ᛶ㸹
㸯㸬⌫ᑐ⛠
㟁ሙ㸹
㸯㸬୰ᚰ㹍ࡢࡲࢃࡾ࡟⌫ᑐ⛠
㸰㸬ᨺᑕ≧࡛୰ᚰ࠿ࡽࡢ㊥㞳ࡢࡳ࡟౫Ꮡ
Ѝ㹍ࢆ୰ᚰ࡜ࡍࡿ༙ᚄ U ࡢ⌫㠃㹑࡟࢞࢘ࢫࡢἲ๎ࢆ㐺⏝
ၥ㢟㸳 ༙ᚄ㹟ࡢ↓㝈࡟㛗࠸෇⟄ࡢ⾲㠃࡟㸪༢఩㛗ࡉ࠶ࡓ
ࡾȢࡢ୍ᵝ࡞㟁Ⲵࡀศᕸࡋ࡚࠸ࡿ࡜ࡁ
㟁Ⲵศᕸࡢᑐ⛠ᛶ㸹
෇⟄ࡢ୰ᚰ㍈࡟ᑐࡋ࡚㸪
㸯㸬ᅇ㌿ᑐ⛠
㸰㸬୪㐍ᑐ⛠
㸱㸬㸰ᅇᑐ⛠
ᕥ㎶㸻
ྑ㎶㸻㹑ෆࡢ㟁Ⲵ㸭H0㸻Ȣl㸭H0
㟁ሙࡣ㸪
㸯㸬୰ᚰ㍈࡟ᆶ┤࡛ᨺᑕ≧
㸰㸬୰ᚰ㍈࠿ࡽࡢ㊥㞳ࡢࡳ࡟౫Ꮡ
ࡋࡓࡀࡗ࡚㸪
Ѝ ┤⥺ࢆ୰ᚰ㍈࡜ࡍࡿ෇⟄≧ࡢ㛢᭤㠃㹑࡟࢞࢘ࢫࡢ
ἲ๎ࢆ㐺⏝
㸯㸫㸳 ᑟయ
ᑟయࡢࡲࢃࡾࡢ㟼㟁ሙ
ᑟయ࡜⤯⦕య
㟼Ṇ≧ែ࡛ࡣ㸪
ᑟయ 㸫 㟁Ẽࢆࡼࡃఏ࠼ࡿ≀㉁㸦㔠ᒓ㸧
⤯⦕య 㸫 㟁Ẽࢆ࡯࡜ࢇ࡝ఏ࠼࡞࠸≀㉁
༙ᑟయ 㸫 ୰㛫ࡢࡶࡢ
㟁Ẽఏᑟ⋡
㸯㸬ᑟయෆ㒊࡟㟁ሙࡣᏑᅾࡋ࡞࠸㸦࠶ࢀࡤ㟁Ꮚࡀ⛣ື㸧
Ѝ ᑟయෆ㒊࡟ṇ࿡ࡢ㟁ⲴࡣᏑᅾࡋ࡞࠸㸬
㸦қ࢞࢘ࢫࡢἲ๎㸧
㖟㸮Υ
™8㸦6P㸧
㖡
™8
㔠
™8
࢞ࣛࢫࢯ࣮ࢲ -9 㹼 -11㸦6P㸧
㞼ẕ
-13
ࢦ࣒
-10 㹼 -15
ࣃࣛࣇ࢕ࣥ
-13 㹼 -17
6L㸪*H
*D$V
㸯 㹼 6㸦6P㸧
㟼㟁ሙ୰ࡢᑟయ⌫㸸ᅗ 㹃
E
ᑟయ(㔠ᒓ) ༙ᑟయ ⤯⦕య
(㔠ᒓ⤖ྜ) (ඹ᭷⤖ྜ) 㸦࢖࢜ࣥ⤖ྜ㸧
⾲㠃࡟㟁Ⲵ Ѝ ㄏᑟ㟁Ⲵ 㹼 㟼㟁ㄏᑟ
ᖏ㟁ࡋࡓᑟయ⌫㸸
ᑟయ⾲㠃ࡢ㟁ሙ࡜㟁Ⲵᐦᗘ
㟁Ⲵᐦᗘ㸹Ȫ㸦ࢸ࢟ࢫࢺ࡛ࡣȰ㸧[C/m2]
Ǽ㹑
෇⟄ᆺࡢ㛢᭤㠃㹑ᗏ㠃✚Ǽ㹑࡟࢞࢘ࢫࡢἲ๎
㹃nrG㹑㸻̿̿Ǽ㹏
ᖏ㟁ࡋࡓᑟయ⌫ࡢ㟁ሙ㸸
H0
㟁Ⲵࡣ⾲㠃࡟⌫㠃ୖ(≧)࡟ศᕸ
ࢆ㐺⏝㸬
ᑐ⛠ᛶ࠿ࡽ㟁ሙࡣᨺᑕ≧
ᕥ㎶㸻㹃Ǽ㹑
⦎⩦ၥ㢟 ༙ᚄ㹟ࡢ⌫㠃ୖ࡟㟁Ⲵ㹏ࡀ୍ᵝ࡟ศᕸࡋ࡚࠸
ࡿ࡜ࡁࡢ㟼㟁ሙࢆồࡵࡼ㸬
㸯
ྑ㎶㸻̿̿ȪǼ㹑
Ȝ0
㹃㸻̿̿
H0
Ȫ
ၥ㢟 11 㟁ሙ୰ࡢཌࡉ㹢ࡢᑟయᯈ