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그리피스 책 10.3장 점전하에 대한 그림파일

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작성자 정준호 작성일20-07-11 22:42 조회337,739회 댓글34건

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올려주셔서 감사합니다.

위의 Lienard–Wiechert potential은 맥스웰 방정식에 뒤처진 퍼텐셜 개념만 더했을 뿐이고, 1898년에 발표되었습니다.
아인슈타인이 특수상대론을 발표한 것은 1905년입니다.
이에 대하여 어떻게 생각하십니까?

뒤처진 퍼텐셜을 사용하여 유도된 11장의 라모 공식이 틀렸다면, 뒤처진 퍼텐셜과 쿨롱 게이지를 부정하시는 것으로 봐도 됩니까?

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댓글 감사합니다. 아인슈타인의 상대성은 Liénard–Wiechert potential과 로렌츠 변환을 이용한 것입니다. 1905년 상대성이론은 전자기학에 대한 내용입니다. 그리고 wikipedia Liénard–Wiechert potential를 검색하시면 자세히 설명되어 있습니다. https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential
내용을 보시고 다시 토론하시는 것이 좋을 것 같습니다.
라모 공식이 무엇이죠? 라머 공식입니까?  저는 비상대론적 라머 공식에서는 아무런 문제가 없다고 생각합니다.

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11장의 라머 공식 유도는 틀렸다고 하셨잖아요.
뒤처진 퍼텐셜 개념이 들어가서 상대론적 전자기학이라고 규정하신 것 같은데요.

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댓글 감사합니다. 아닙니다. 11장이 문제가 아니라 11.2장에서부터 문제가 있다고 한 것같은데요? 이 책이 좀 그렇습니다.
로렌츠힘에 대한 코멘트도 남겨주시면 감사하겠습니다.

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꼬투리 잡지 마시고;;
11.2장에서 유도한 라머 공식은 상대론적이라 틀렸다면서요.

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댓글 감사합니다. 예, 맞습니다. 11.2장은 상대론적이라 틀렸다고 했습니다. 그러나 11.1은 틀렸다고 말한 적 없습니다. 질문에 11장의 라머공식이 틀렸다고 질문하셨기에 구체적으로 구분한 것뿐입니다.

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11.2장의 라머 공식이 틀렸다면
맥스웰 방정식에 뒤처진 퍼텐셜 개념을 추가로 도입한 것이 문제란 얘기인 것 같은데 맞습니까?

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댓글 감사합니다. 아닙니다. 뒤처진 퍼텐셜은 상대성이 없습니다. 그래서 아무런 문제도 없습니다. 하지만 식(10.43)을 보시면 상대성 개념이 들어 있습니다. 확인 부탁드립니다.

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뒤처진 퍼텐셜이 문제가 아니라면
유도과정에서 어떤 개념을 도입하면서 상대성이 생겼다는 것인지 설명해 주십시오.

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댓글 감사합니다. 식 (10.43)을 보시면 기차의 겉보기 체적 tau' 이 실제 체적과 관련되어 있는데 그것이 길이 수축을 이용했고요, Example 10.3를 보시면 점전하는 등속운동한다고 했는데 식(10.59)을 보시면 속도를 미분했습니다. 만약에 앞의 속도와 식(10.59)의 속도가 다르면 어느 속도를 말하는 것이죠? 저는 모르겠습니다.
마지막으로 제 견해를 말하면 3차원에서는 시간은 스칼라양입니다. 그런데 4차원인 경우는 시간이 벡터량으로 사용되고 있습니다. 만약에 시간이 벡터량이면 벡터*벡터(벡터곱)는 있어도 벡터/벡터(벡터 나눗셈)의 물리량은 없습니다. 그래서 3차원에서는 그런 용어가 없습니다. 그런데 10.3.2장은 속도를 미분해서 가속도도 있고 시간벡터도 있고 그래서 총체적으로 문제가 있습니다. 그렇다보니 식(10.72)을 보시면 가속도가 있는데 어느 전하의 가속도인지 모르겠습니다. 앞에서 전하의 속도는 등속도라고 했는데 이 전하 말고 또 다른 전하가 있나요? 그러면 그 전하의 가속운동 하나요? 저는 모르겠습니다. 그래서 사실 그리피스 책이 좀 그렇습니다.

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틀렸다가 아니라 이해가 안간다... 입니까?

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10.3.1 에서 점전하의 일반적인 운동에 대하여 전기 및 자기 퍼텐셜을 유도하였고
Example 10.3은 특수한 경우로써 등속운동시 퍼텐셜이 어떻게 되는지 확인하라는 문제인데
10.3.2 에서 다시 일반적인 운동에 대하여 전기장 및 자기장을 유도하는 것과 무슨 상관이죠?

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그리고 10.3.2 장에 시간벡터 따위는 없는데, 설마 그라디언트를 모르시는 건가요?
10.3 전체가 점전하를 다루고 있고,
10.72 식의 가속도는 당연히 그 점전하의 가속도입니다.

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댓글 감사합니다. 제가 앞에서 설명해드렸습니다. 길이수축이 도입되면서 상대성이 생겼다고 했습니다.

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p452. 하단의 12번 주석을 읽어보시겠습니까?

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댓글 감사합니다. 읽어 보니 특수 상대성과 로렌츠 수축과는 상관이 없다고 하네요. 하지만 다소 도플러 효과를 연상시킨다고 하는데, 도플러 효과에서도 길이가 평창 합니까? 길이 수축이 아니라 이것은 길이 팽창이 일어난 경우이네요. 그러면 상대성도 아니고 고전적으로는 길이수축과 팽창은 일어나지 않는데 이 경우는 무슨 경우인지 모르겠습니다. 어쨌든 도플러 효과 처럼 식(10.43)이 사용되었네요. 그리고 기차는 Example 10.3에서는 점전하인데 부피가 필요한가요? 아마 필요없을 것 같은데 그런데 왜 식 (10.44)를 사용하고 있습니까?  그리고 전하의 속도는 등속도 운동인데 식 (10.72)에 왜 가속도가 나오는지 모르겠습니다. 아시면 설명 부탁드립니다.

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10.3장은 점전하의 임의의 운동을 다루고 있습니다. 등속운동으로 한정하지 않았습니다.
Example 10.3 에서 특별히 등속운동의 경우 식이 어떻게 되는지 풀어본 것일 뿐입니다.

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댓글 감사합니다. 그렇다면 가속운동하는 전하는 어디에 있습니까? 그리고 식 (10.42)에 있는 속도는 비등속도 운동입니까? 아니면 등속도 운동입니까? 그것을 이해하신 후에 질문 부탁드립니다.

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가속운동하는 전하가 어디에 있다뇨.
10.3.1 처음에 궤적 w(t)=position of q at time t 라고 정의했잖아요.
가속을 하든 등속으로 가든 정지하든 그 어떤 궤적이라도 표현할 수 있도록 일반화한 수식으로 시작하잖아요.
저 궤적을 등속직선으로 설정하면 그에 따른 퍼텐셜과 장을 얻을 수 있는거고
가속으로 설정하면 그에 맞는 퍼텐셜과 장이 나오게 되는거죠...
이런걸 설명해야 합니까?

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그리고 (10.42) 윗줄에 v is the velocity of the charge at the retarded time 이라고 나와있잖아요.
등속운동을 가정했으면 굳이 특정 시점의 속도라고 썼겠습니까?

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댓글 감사합니다. 맞습니다. 그렇지만 그 궤적의 전하는 등속운동하는 전하와 가속도 운동하는 전하에 대한 구분이 있어야 하지 않나요? 이 책의 문제점은 그점입니다. 전하의 속도에 대한 구체적 구별이 없이 v로만 사용한다는 겁니다.
식(10.42) 윗줄에 v is the velocity of the charge at the retarded time가 있습니다. 그렇다면 식(10.43)의 속도는 무엇입니까? 그림 10.7의 속도가 비등속도 운동합니까? 그러면 가속운동하는데... 도플러 효과에서 가속운동에 대한 내용은 없는 것으로 알고 있습니다. 그리고 point charge가 체적이 필요합니까? 물리에서 point charge 또는 point mass라는 용어를 사용하는 순간 그 물체의 체적은 무시되는데...
다시 한번 검토하시고 댓글 부탁드립니다.

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혹시 순간속도를 모르십니까.
그냥 수학적 기초가 너무 부실하셔서 책 이해를 못한다는게 결론이네요.

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댓글 감사합니다. 일반적으로 속도라는 말은 순간속도라고 합니다. 평균속도는 특화되어 있기 때문에 반드시 평균속도라고 합니다. 그러니 우리가 말하고 있는 속도는 순간속도 입니다. 그리고 등속도도 순간속도입니다. 물리를 이해하시는데 도움이 되었으면 좋겠습니다.

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순간속도를 아시는분이 등속운동의 속도와 비등속운동의 속도를 구분하나요?

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댓글 감사합니다. 무슨 말씀을 하시는지요?

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순간속도가 포함된 식을 두고
등속운동인지 비등속운동인지 구체적으로 구별해야 한다면서요

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댓글 감사합니다. 순간속도를 구하고 그 순간속도에서 다시 미분해서 가속도가 상수이면 비등속운동이고요, 가속도가 영이면 등속운동이라고 합니다.
그래서 순간속도의 값이 시간의 함수이면 비등속도 운동이고요, 시간의 함수가 아니면 등속운동입니다.

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공부해오셨네요.
책에 답이 있는데 왜 물으셨습니까?

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댓글 감사합니다. 아직 이해하지 못하신 것 같아서 올린 글입니다. 그리고 조만간에 운동의 정의를 유튜브에 올텐데 그 때 동영상 보시면 많은 도움이 되실 겁니다.

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책 내용을 모르겠다고 한건 제가 아니라 님인데요...

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Katina님의 댓글

Katina 작성일

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Georgette님의 댓글

Georgette 작성일

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Lauren님의 댓글

Lauren 작성일

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https://www.adidas-superstars.us.com/ Adidas Superstar Women
https://www.adidass.us.com/ Adidas Outlet
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https://www.yeezy350shoes.ca/ Yeezy Boost 350 V2
https://www.adidas-originalssuperstar.us.com/ Adidas Superstar Men
https://www.pandoras.uk.com/ Pandora Charms
https://www.adidasyeezyofficialwebsite.us.com/ Adidas Yeezy Official Website
https://www.ultra-boost.us.com/ Adidas Ultra Boost
https://www.nike-onlinecanada.ca/ Nike Canada Online Shopping
https://www.airforce1s.us.com/ Air Force 1
https://www.adidassuperstars.us.com/ Adidas Superstar Shoes
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https://www.adidasstoreonline.us.com/ Adidas Store
https://www.adidasoutletstores.us.com/ Adidas Outlet Store
https://www.nikeclearancestores.us.com/ Nike Clearance
https://www.adidasyeezys.us.com/ Adidas Yeezys
https://www.trainersoutlet.uk.com/ Adidas Trainers
https://www.adidascom.us.com/ Adidas Shoes
https://www.adidasoutletshoes.us.com/ Adidas Outlet
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https://www.jewelrypandora.us.org/ Pandora
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https://www.offwhite-shoes.us.com/ Off White Jordan 1
https://www.yeezysboost-350.us.com/ Yeezy 350
https://www.ultraboost.uk.com/ Ultra Boost
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https://www.officialyeezywebsite.us.com/ Yeezy
https://www.pandorasjewelry.uk.com/ Pandora UK
https://www.yeezyshop.us.com/ Adidas Yeezy
https://www.newtrainers.uk.com/ Adidas Trainers
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https://www.nikesneakersstore.us.com/ Nike Sneakers Men
https://www.yeezy500boost.us.com/ Yeezy 500
https://www.nike-sneakers.us.com/ Nike Sneakers
https://www.nikeshoesoutlets.us.com/ Nike Outlet Shoes
https://www.nikepresto.us.org/ Nike Presto
https://www.pandoracharmsbracelets.us.com/ Pandora Charms
https://www.yeezycanadastore.ca/ Yeezy
https://www.shoesoutletstores.ca/ Nike
https://www.yeezyshoesboost.us.com/ Yeezy Boost
https://www.nikesrunningshoes.us.com/ Nike Running Shoes
https://www.nmd.uk.com/ Adidas NMD
https://www.yeezyshoesadidas.us.com/ Adidas Yeezy
https://pandorabracelets-charms.us.com/ Pandora Charms
https://www.nikeoutlet--store.us.com/ Nike Outlet
https://www.yeezyboost350v2.us.com/ Yeezy 350
https://www.trainersstore.uk.com/ Nike UK
https://www.outletadidasshoes.us.com/ Adidas Outlet Online
https://www.nikeair-force1.us.com/ Nike Air Force 1 Mid
https://www.nikecanada-onlineshopping.ca/ Nike Canada
https://www.adidasshoesshop.us.com/ Adidas Shoes
https://www.nikeshoesshop.ca/ Nike Canada
https://www.nikesoutlets.us.com/ Nikes
https://www.nike-rosherun.us.com/ Roshe
https://www.pandoracharmsbracelet.us.com/ Pandora Bracelet Charms
https://www.newadidasshoes.us.com/ Adidas Shoes
https://www.nmdsadidas.us.com/ NMD
https://www.yeezyshoesstore.ca/ Yeezy
https://www.nikeoutletstores.us.com/ Nike Outlet

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