Question

Define drift velocity and derive an expression for it . 2 Derive the expression 1=nAevd.
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Answer 1

Explanation:

Drift velocity is defined as the average velocity attained by the particles (electrons) of a given material due to an electric field that is proportional to current.

Answer 2

$\boxed { \displaystyle \rm \blue{Answer.}}$

ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴀᴛᴛᴀɪɴᴇᴅ ʙʏ ᴛʜᴇ ᴘᴀʀᴛɪᴄʟᴇs (ᴇʟᴇᴄᴛʀᴏɴs) ᴏғ ᴀ ɢɪᴠᴇɴ ᴍᴀᴛᴇʀɪᴀʟ ᴅᴜᴇ ᴛᴏ ᴀɴ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴛʜᴀᴛ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴄᴜʀʀᴇɴᴛ. ᴏʜᴍ’s ʟᴀᴡ ᴄᴀɴ ʙᴇ ᴇxᴘʀᴇssᴇᴅ ɪɴ ᴛᴇʀᴍs ᴏғ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴀs ғᴏʟʟᴏᴡs:

ᴜ=μᴇ

ᴡʜᴇʀᴇ,

ᴜ: ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ (ᴍ/s)

μ: ᴍᴀᴛᴇʀɪᴀʟ’s ᴇʟᴇᴄᴛʀᴏɴ ᴍᴏʙɪʟɪᴛʏ (ᴍ2/ᴠ.s)

ᴇ: ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ (ᴠ/ᴍ)

ᴅᴇʀɪᴠᴀᴛɪᴏɴ ᴏғ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ

ғᴏʟʟᴏᴡɪɴɢ ɪs ᴛʜᴇ ᴅᴇʀɪᴠᴀᴛɪᴏɴ ᴏғ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ:

ғ=−μᴇ ᴀ=ғᴍ=−μᴇᴍ ᴜ=ᴠ+ᴀᴛ

ʜᴇʀᴇ,

ᴠ = 0

ᴛ = ᴛ (ʀᴇʟᴀxᴀᴛɪᴏɴ ᴛɪᴍᴇ ᴛʜᴀᴛ ɪs ᴛʜᴇ ᴛɪᴍᴇ ʀᴇϙᴜɪʀᴇᴅ ʙʏ ᴀɴ ᴇʟᴇᴄᴛʀᴏɴ ᴛᴏ ʀᴇᴛᴜʀɴ ᴛᴏ ɪᴛs ɪɴɪᴛɪᴀʟ ᴇϙᴜɪʟɪʙʀɪᴜᴍ ᴠᴀʟᴜᴇ)

ᴜ=ᴀᴛ (sᴜʙsᴛɪᴛᴜᴛɪɴɢ ғᴏʀ ᴠ ᴀɴᴅ ᴜ)

∴ᴜ=(−μᴇᴍ)ᴛ (sᴜʙsᴛɪᴛᴜᴛɪɴɢ ғᴏʀ ᴀ)

ᴛʜɪs ɪs ᴛʜᴇ ғɪɴᴀʟ ᴇϙᴜᴀᴛɪᴏɴ ᴇxᴘʟᴀɪɴɪɴɢ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ.

ʙᴜᴛ ᴀs ᴛʜᴇ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ ɪɴᴄʀᴇᴀsᴇs, ᴛʜᴇ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴇʟᴇᴄᴛʀᴏɴs ɪɴᴄʀᴇᴀsᴇs ɪɴ ᴀ ᴍᴇᴛᴀʟʟɪᴄ ᴄᴏɴᴅᴜᴄᴛᴏʀ.

2) ʟᴇᴛ ɴᴏ. ᴏғ ᴇʟᴇᴄᴛʀᴏɴs ᴘᴇʀ ᴜɴɪᴛ ᴠᴏʟᴜᴍᴇ=ɴ

ᴄʜᴀʀɢᴇ ᴏɴ ᴀɴ ᴀᴛᴏᴍ=ᴇ

ɴᴏ.ᴏғ ᴇʟᴇᴄᴛʀᴏɴs ɪɴ ʟᴇɴɢᴛʜ ʟ ᴏғ ᴛʜᴇ

ᴄᴏɴᴅᴜᴄᴛᴏʀ=ɴ×ᴠᴏʟᴜᴍᴇ ᴏғ ᴄᴏɴᴅᴜᴄᴛᴏʀ=ɴᴀʟ

ᴛᴏᴛᴀʟ ᴄʜᴀʀɢᴇ ᴄᴏɴᴛᴀɪɴᴇᴅ ɪɴ ᴛʜᴇ ᴄᴏɴᴅᴜᴄᴛᴏʀ ɪs

ϙ = ɴᴇᴀʟ

ᴀʟʟ ᴛʜᴇ ᴇʟᴇᴄᴛʀᴏɴs ᴡʜɪᴄʜ ᴇɴᴛᴇʀ ᴛʜᴇ ᴄᴏɴᴅᴜᴄᴛᴏʀ ᴀᴛ ᴛʜᴇ ʀɪɢʜᴛ ᴇɴᴅ ᴡɪʟʟ ᴘᴀss ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ʟᴇғᴛ ᴇɴᴅ ᴏғ ᴛʜᴇ ᴄᴏɴᴅᴜᴄᴛᴏʀ ɪɴ ᴛɪᴍᴇ,

ᴛ = ᴅɪsᴛᴀɴᴄᴇ/ᴠᴇʟᴏᴄɪᴛʏ

=ʟ/ᴠᴅ

ᴛʜᴇʀᴇғᴏʀᴇ,ᴄᴜʀʀᴇɴᴛ,

ɪ=ϙ/ᴛ=ᴇɴᴀʟ/(ʟ/ᴠᴅ)

=> ɪ=ɴᴇᴀᴠᴅ

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