electric field at center of sphere having surfcae vcharge ar
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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️Spherical shell is an equipotential surface. ... the charge that placed inside the shell will have its own electric field. ... What is the the electric field inside an uncharged conducting shell if a point charge Q resides at its centre..
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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️Spherical shell is an equipotential surface. ... the charge that placed inside the shell will have its own electric field. ... What is the the electric field inside an uncharged conducting shell if a point charge Q resides at its centre..
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ʏᴏᴜ sᴇᴇᴍ ᴛᴏ ʙᴇ ᴄᴏɴғᴜsᴇᴅ ᴀʙᴏᴜᴛ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏғ ᴛʜᴇ ʟɪᴍɪᴛ, ᴡʜɪᴄʜ ɪs ɴᴏʀᴍᴀʟʟʏ ᴄᴏᴠᴇʀᴇᴅ ɪɴ ᴄᴀʟᴄᴜʟᴜs ᴄᴏᴜʀsᴇs. ɪғ ʏᴏᴜ ʜᴀᴠᴇ, ɴᴏᴛ ᴀ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇ, ʙᴜᴛ ᴀ ᴠᴏʟᴜᴍᴇ ᴏғ ᴄʜᴀʀɢᴇ ᴡɪᴛʜ sᴏᴍᴇ ᴅᴇɴsɪᴛʏ ρ, ᴛʜᴇɴ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴇɴᴄʟᴏsᴇᴅ ɪɴ ᴀ sᴍᴀʟʟ sᴘʜᴇʀᴇ ᴡɪᴛʜ ʀᴀᴅɪᴜs ʀ ɪsᴅǫ=ρᴅᴠ=ρ⋅4π3ʀ3
ᴀɴᴅ ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴀᴛ ᴛʜᴇ sᴜʀғᴀᴄᴇ ᴏғ ᴛʜᴇ sᴘʜᴇʀᴇ ᴡɪʟʟ ʙᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏᴇ∝ᴅǫʀ2∝ρʀ3ʀ2=ρʀ.
ᴛʜɪs ғɪᴇʟᴅ ᴍᴀɢɴɪᴛᴜᴅᴇ ɪs ᴡᴇʟʟ-ʙᴇʜᴀᴠᴇᴅ ɪɴ ᴛʜᴇ ʟɪᴍɪᴛ ᴛʜᴀᴛ ʀ ɪs ᴠᴇʀʏ sᴍᴀʟʟ.
ᴛʜᴇ ᴢᴇʀᴏ-sɪᴢᴇ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇ, ᴢᴇʀᴏ-ᴛʜɪᴄᴋɴᴇss sᴜʀғᴀᴄᴇ ᴄʜᴀʀɢᴇ, ᴇᴛᴄ. ᴀʀᴇ ᴜsᴇғᴜʟ ᴀᴘᴘʀᴏxɪᴍᴀᴛɪᴏɴs ᴡʜᴇɴ ᴛʜᴇ sɪᴢᴇ ᴏғ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ɪs ᴍᴜᴄʜ sᴍᴀʟʟᴇʀ ᴛʜᴀɴ ᴛʜᴇ sɪᴢᴇ ᴏғ ᴛʜᴇ ғɪᴇʟᴅ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ᴛʜᴀᴛ ʏᴏᴜ ᴄᴀʀᴇ ᴀʙᴏᴜᴛ. ᴘʜʏsɪᴄᴀʟ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇs, sᴜʀғᴀᴄᴇ ᴄʜᴀʀɢᴇs, ᴀɴᴅ ʟɪɴᴇ ᴄʜᴀʀɢᴇs ᴀʀᴇ ᴀʟʟ ᴀᴄᴛᴜᴀʟʟʏ ᴅɪsᴛʀɪʙᴜᴛᴇᴅ ᴏᴠᴇʀ ᴀ ғɪɴɪᴛᴇ ᴠᴏʟᴜᴍᴇ. ᴇᴠᴇɴ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴏғ ᴀ sɪɴɢʟᴇ ᴇʟᴇᴄᴛʀᴏɴ ɪs ᴅɪsᴛʀɪʙᴜᴛᴇᴅ ᴏᴠᴇʀ ᴀ ғɪɴɪᴛᴇ ᴠᴏʟᴜᴍᴇ, ᴛʜᴀɴᴋs ᴛᴏ ǫᴜᴀɴᴛᴜᴍ-ᴍᴇᴄʜᴀɴɪᴄᴀʟ ᴜɴᴄᴇʀᴛᴀɪɴᴛʏ ɪɴ ᴛʜᴇ ᴇʟᴇᴄᴛʀᴏɴ's ᴘᴏsɪᴛɪᴏɴ.
ʏᴏᴜ sᴇᴇᴍ ᴛᴏ ʙᴇ ᴄᴏɴғᴜsᴇᴅ ᴀʙᴏᴜᴛ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏғ ᴛʜᴇ ʟɪᴍɪᴛ, ᴡʜɪᴄʜ ɪs ɴᴏʀᴍᴀʟʟʏ ᴄᴏᴠᴇʀᴇᴅ ɪɴ ᴄᴀʟᴄᴜʟᴜs ᴄᴏᴜʀsᴇs. ɪғ ʏᴏᴜ ʜᴀᴠᴇ, ɴᴏᴛ ᴀ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇ, ʙᴜᴛ ᴀ ᴠᴏʟᴜᴍᴇ ᴏғ ᴄʜᴀʀɢᴇ ᴡɪᴛʜ sᴏᴍᴇ ᴅᴇɴsɪᴛʏ ρ, ᴛʜᴇɴ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴇɴᴄʟᴏsᴇᴅ ɪɴ ᴀ sᴍᴀʟʟ sᴘʜᴇʀᴇ ᴡɪᴛʜ ʀᴀᴅɪᴜs ʀ ɪsᴅǫ=ρᴅᴠ=ρ⋅4π3ʀ3
ᴀɴᴅ ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴀᴛ ᴛʜᴇ sᴜʀғᴀᴄᴇ ᴏғ ᴛʜᴇ sᴘʜᴇʀᴇ ᴡɪʟʟ ʙᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏᴇ∝ᴅǫʀ2∝ρʀ3ʀ2=ρʀ.
ᴛʜɪs ғɪᴇʟᴅ ᴍᴀɢɴɪᴛᴜᴅᴇ ɪs ᴡᴇʟʟ-ʙᴇʜᴀᴠᴇᴅ ɪɴ ᴛʜᴇ ʟɪᴍɪᴛ ᴛʜᴀᴛ ʀ ɪs ᴠᴇʀʏ sᴍᴀʟʟ.
ᴛʜᴇ ᴢᴇʀᴏ-sɪᴢᴇ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇ, ᴢᴇʀᴏ-ᴛʜɪᴄᴋɴᴇss sᴜʀғᴀᴄᴇ ᴄʜᴀʀɢᴇ, ᴇᴛᴄ. ᴀʀᴇ ᴜsᴇғᴜʟ ᴀᴘᴘʀᴏxɪᴍᴀᴛɪᴏɴs ᴡʜᴇɴ ᴛʜᴇ sɪᴢᴇ ᴏғ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ɪs ᴍᴜᴄʜ sᴍᴀʟʟᴇʀ ᴛʜᴀɴ ᴛʜᴇ sɪᴢᴇ ᴏғ ᴛʜᴇ ғɪᴇʟᴅ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ᴛʜᴀᴛ ʏᴏᴜ ᴄᴀʀᴇ ᴀʙᴏᴜᴛ. ᴘʜʏsɪᴄᴀʟ ᴘᴏɪɴᴛ ᴄʜᴀʀɢᴇs, sᴜʀғᴀᴄᴇ ᴄʜᴀʀɢᴇs, ᴀɴᴅ ʟɪɴᴇ ᴄʜᴀʀɢᴇs ᴀʀᴇ ᴀʟʟ ᴀᴄᴛᴜᴀʟʟʏ ᴅɪsᴛʀɪʙᴜᴛᴇᴅ ᴏᴠᴇʀ ᴀ ғɪɴɪᴛᴇ ᴠᴏʟᴜᴍᴇ. ᴇᴠᴇɴ ᴛʜᴇ ᴄʜᴀʀɢᴇ ᴏғ ᴀ sɪɴɢʟᴇ ᴇʟᴇᴄᴛʀᴏɴ ɪs ᴅɪsᴛʀɪʙᴜᴛᴇᴅ ᴏᴠᴇʀ ᴀ ғɪɴɪᴛᴇ ᴠᴏʟᴜᴍᴇ, ᴛʜᴀɴᴋs ᴛᴏ ǫᴜᴀɴᴛᴜᴍ-ᴍᴇᴄʜᴀɴɪᴄᴀʟ ᴜɴᴄᴇʀᴛᴀɪɴᴛʏ ɪɴ ᴛʜᴇ ᴇʟᴇᴄᴛʀᴏɴ's ᴘᴏsɪᴛɪᴏɴ.
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