Write derivation of electric field due to uniformly charged hollow sphere.
Answers
ᴄᵒⁿˢⁱᵈᵉʳ ᵃ ᵗʰⁱⁿ ˢᵖʰᵉʳⁱᶜᵃˡ ˢʰᵉˡˡ ᵒᶠ ʳᵃᵈⁱᵘˢ ʀ ʷⁱᵗʰ ᵃ ᵖᵒˢⁱᵗⁱᵛᵉ ᶜʰᵃʳᵍᵉ ᵠ ᵈⁱˢᵗʳⁱᵇᵘᵗᵉᵈ ᵘⁿⁱᶠᵒʳᵐˡʸ ᵒⁿ ᵗʰᵉ ˢᵘʳᶠᵃᶜᵉ. ᴀˢ ᵗʰᵉ ᶜʰᵃʳᵍᵉ ⁱˢ ᵘⁿⁱᶠᵒʳᵐˡʸ ᵈⁱˢᵗʳⁱᵇᵘᵗᵉᵈ, ᵗʰᵉ ᵉˡᵉᶜᵗʳⁱᶜ ᶠⁱᵉˡᵈ ⁱˢ ˢʸᵐᵐᵉᵗʳⁱᶜᵃˡ ᵃⁿᵈ ᵈⁱʳᵉᶜᵗᵉᵈ ʳᵃᵈⁱᵃˡˡʸ ᵒᵘᵗʷᵃʳᵈ.
(ⁱ) ᴇˡᵉᶜᵗʳⁱᶜ ᶠⁱᵉˡᵈ ᵒᵘᵗˢⁱᵈᵉ ᵗʰᵉ ˢʰᵉˡˡ:
ғᵒʳ ᵖᵒⁱⁿᵗ ʳ>ʀ; ᵈʳᵃʷ ᵃ ˢᵖʰᵉʳⁱᶜᵃˡ ᵍᵃᵘˢˢⁱᵃⁿ ˢᵘʳᶠᵃᶜᵉ ᵒᶠ ʳᵃᵈⁱᵘˢ ʳ.
ᴜˢⁱⁿᵍ ᵍᵃᵘˢˢ ˡᵃʷ, ∮ᴇ.ᵈˢ=
ᵠ
0
ᵠ
ᵉⁿᵈ
sⁱⁿᶜᵉ
ᴇ
ⁱˢ ᵖᵉʳᵖᵉⁿᵈⁱᶜᵘˡᵃʳ ᵗᵒ ᵍᵃᵘˢˢⁱᵃⁿ ˢᵘʳᶠᵃᶜᵉ, ᵃⁿᵍˡᵉ ᵇᵉᵗʷᵉᵉ
ᴇ
ⁱˢ 0.
ᴀˡˢᵒ
ᴇ
ᵇᵉⁱⁿᵍ ᶜᵒⁿˢᵗᵃⁿᵗ, ᶜᵃⁿ ᵇᵉ ᵗᵃᵏᵉⁿ ᵒᵘᵗ ᵒᶠ ⁱⁿᵗᵉᵍʳᵃˡ.
sᵒ, ᴇ(4πʳ
2
)=
ᵠ
0
ᵠ
sᵒ, ᴇ=
4πε
0
1
ʳ
2
ᵠ
ᴛʰᵘˢ ᵉˡᵉᶜᵗʳⁱᶜ ᶠⁱᵉˡᵈ ᵒᵘᵗˢⁱᵈᵉ ᵃ ᵘⁿⁱᶠᵒʳᵐˡʸ ᶜʰᵃʳᵍᵉᵈ ˢᵖʰᵉʳⁱᶜᵃˡ ˢʰᵉˡˡ ⁱˢ ˢᵃᵐᵉ ᵃˢ ⁱᶠ ᵃˡˡ ᵗʰᵉ ᶜʰᵃʳᵍᵉ ᵠ ʷᵉʳᵉ ᶜᵒⁿᶜᵉⁿᵗʳᵃᵗᵉᵈ ᵃˢ ᵃ ᵖᵒⁱⁿᵗ ᶜʰᵃʳᵍᵉ ᵃᵗ ᵗʰᵉ ᶜᵉⁿᵗᵉʳ ᵒᶠ ᵗʰᵉ ˢʰᵉˡˡ.
(ⁱⁱ) ɪⁿˢⁱᵈᵉ ᵗʰᵉ ˢʰᵉˡˡ:
ɪⁿ ᵗʰⁱˢ ᶜᵃˢᵉ, ʷᵉ ˢᵉˡᵉᶜᵗ ᵃ ᵍᵃᵘˢˢⁱᵃⁿ ˢᵘʳᶠᵃᶜᵉ ᶜᵒⁿᶜᵉⁿᵗʳⁱᶜ ʷⁱᵗʰ ᵗʰᵉ ˢʰᵉˡˡ ᵒᶠ ʳᵃᵈⁱᵘˢ ʳ (ʳ>ʀ).
sᵒ, ∮ᴇ.ᵈˢ=ᴇ(4πʳ
2
)
ᴀᶜᶜᵒʳᵈⁱⁿᵍ ᵗᵒ ᵍᵃᵘˢˢ ˡᵃʷ,
ᴇ(4πʳ
2
)=
ε
0
ϙ
ᵉⁿᵈ
sⁱⁿᶜᵉ ᶜʰᵃʳᵍᵉ ᵉⁿᶜˡᵒˢᵉᵈ ⁱⁿˢⁱᵈᵉ ᵗʰᵉ ˢᵖʰᵉʳⁱᶜᵃˡ ˢʰᵉˡˡ ⁱˢ ᶻᵉʳᵒ.
sᵒ, ᴇ=0
ʜᵉⁿᶜᵉ, ᵗʰᵉ ᵉˡᵉᶜᵗʳⁱᶜ ᶠⁱᵉˡᵈ ᵈᵘᵉ ᵗᵒ ᵃ ᵘⁿⁱᶠᵒʳᵐˡʸ ᶜʰᵃʳᵍᵉᵈ ˢᵖʰᵉʳⁱᶜᵃˡ ˢʰᵉˡˡ ⁱˢ ᶻᵉʳᵒ ᵃᵗ ᵃˡˡ ᵖᵒⁱⁿᵗˢ ⁱⁿˢⁱᵈᵉ ᵗʰᵉ ˢʰᵉˡˡ
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Answer:
Consider a thin spherical shell of radius R with a positive charge q distributed uniformly on the surface. As the charge is uniformly distributed, the electric field is symmetrical and directed radially outward.
Explanation:
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