Question

Derive formula for Drift velocity.

( Class -12 - Physics) ​

Answer 1

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$\huge {\mathfrak {\purple {Q.}}}}$Derive formula for Drift velocity.

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ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ғᴏʀᴍᴜʟᴀ

ᴛʜɪs ғᴏʀᴍᴜʟᴀ ɪs ᴜsᴇᴅ ᴛᴏ ғɪɴᴅ ᴛʜᴇ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴇʟᴇᴄᴛʀᴏɴs ɪɴ ᴀ ᴄᴜʀʀᴇɴᴛ-ᴄᴀʀʀʏɪɴɢ ᴄᴏɴᴅᴜᴄᴛᴏʀ. ᴡʜᴇɴ ᴇʟᴇᴄᴛʀᴏɴs ᴡɪᴛʜ ᴅᴇɴsɪᴛʏ ɴ ᴀɴᴅ ᴄʜᴀʀɢᴇ ϙ ᴄᴀᴜsᴇs ᴀ ᴄᴜʀʀᴇɴᴛ 'ɪ' ᴛᴏ ғʟᴏᴡ ᴛʜʀᴏᴜɢʜ ᴀ ᴄᴏɴᴅᴜᴄᴛᴏʀ ᴏғ ᴄʀᴏss-sᴇᴄᴛɪᴏɴᴀʟ ᴀʀᴇᴀ ᴀ, ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴠ ᴄᴀɴ ʙᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ɪ = ɴᴀᴠϙ.

(ɪ) ᴡʜᴇɴ ᴄᴏɴᴅᴜᴄᴛᴏʀ ɪs sᴜʙᴊᴇᴄᴛᴇᴅ ᴛᴏ ᴀɴ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴇ, ᴇᴀᴄʜ ᴇʟᴇᴄᴛʀᴏɴ ᴇxᴘᴇʀɪᴇɴᴄᴇ ᴀ ғᴏʀᴄᴇ.

ғ=-ᴇᴇ

ᴀɴᴅ ᴀᴄϙᴜɪʀᴇs ᴀɴ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ

ᴀ = ғ/ᴍ = - ᴇᴇ/ᴍ -----(ɪ)

ʜᴇʀᴇ ᴍ = ᴍᴀss ᴏғ ᴇʟᴇᴄᴛɪᴏɴ, ᴇ = ᴄʜᴀʀɢᴇ, ᴇ = ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ.

ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴛɪᴍᴇ ᴅɪғғᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴄᴏʟʟɪsɪᴏɴs ɪs ᴋɴᴏᴡɴ ᴀs ʀᴇʟᴀxᴀᴛɪᴏɴ ᴛɪᴍᴇ ᴏғ ᴇʟᴇᴄᴛɪᴏɴ.

$As, v=u+at from eq of motion$

$\tt the drift velocity ^d is defined as$

$\tt v^d= \frac{v^1+v^2+....v^n}{n}$

$\tt v^d= \frac{(u^1+u^2+....u^n)+a(π^1π^2...π^n)}{n}$

$\tt v^d= 0 +\frac{(u^1+u^2+....u^n)+a(π^1π^2...π^n)}{n}$

$(average thermal velocity=0)$

$\tt\implies v^d=0+aπ$

$v^d=-\frac{eE}{m}π$. ............{from 1 and 2}

(ɪɪ) ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴇxᴘʀᴇssɪᴏɴ, ʀᴇʟᴀxᴀᴛɪᴏɴ ᴛɪᴍᴇ ɪs ᴛʜᴇ ᴛɪᴍᴇ ɪɴᴛᴇʀᴠᴀʟ ʙᴇᴛᴡᴇᴇɴ sᴜᴄᴄᴇssɪᴠᴇ ᴄᴏʟʟɪsɪᴏɴs ᴏғ ᴀɴ ᴇʟᴇᴄᴛʀᴏɴ ᴏɴ ɪɴᴄʀᴇᴀsɪɴɢ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ, ᴛʜᴇ ᴇʟᴇᴄᴛʀᴏɴs ᴍᴏᴠᴇ ғᴀsᴛᴇʀ ᴀɴᴅ ᴍᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴs ᴏᴄᴄᴜʀ ϙᴜɪᴄᴋʟʏ. ʜᴇɴᴄᴇ, ʀᴇʟᴀxᴀᴛɪᴏɴ ᴛɪᴍᴇ ᴅᴇᴄʀᴇᴀsᴇs ᴡɪᴛʜ ɪɴᴄʀᴇᴀsᴇ ɪɴ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ ᴡʜɪᴄʜ ɪᴍᴘʟɪᴇs ᴛʜᴀᴛ ᴅʀɪғᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴀʟsᴏ ᴅᴇᴄʀᴇᴀsᴇs ᴡɪᴛʜ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ.

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#ʙᴇ ʙʀᴀɪɴʟʏ

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Answer 2

Answer:

This formula is used to find the drift velocity of electrons in a current-carrying conductor. When electrons with density n and charge Q causes a current 'I' to flow through a conductor of cross-sectional area A, Drift velocity v can be calculated through the formula I = nAvQ.

Explanation:

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