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A tiny spherical oil drop carrying a net...

A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength `(81pi)/(7)xx10^5Vm^-1`. When the field is switched off, the drop is observed to fall with terminal velocity `2xx10^-3ms^-1`. Given `g=9.8ms^-2`, viscoisty of the air `=1.8xx10^-5Nsm^-2` and the denisty of oil `=900kg m^-3`, the magnitude of q is

A

(a) `1.6xx10^-19C`

B

(b) `3.2xx10^-19C`

C

(c) `4.8xx10^-19C`

D

(d) `8.0xx10^-19C`

Text Solution

Verified by Experts

The correct Answer is:
D
When the electric field is on
Force due to electric field=weight
`qE=mg`
`qE=4/3piR^3rhog` `:.` `q=(4piR^3rhog)/(3E)` …(i)
When the electric field is switched off
Weight=viscous drag force
`mg=6pietaRv_t`
`4/3piR^3rhog=6pietaRv_t` `:.` `R=sqrt((9etav_t)/(2rhog))` ...(ii)
From (i) & (ii) `q=4/3pi[(9etav_t)/(2rhog)]^(3/2)xx(rhog)/(E)`
`=4/3xxpi[(9xx1.8xx10^-5xx2xx10^-3)/(2xx900xx9.8)]^(3/2)xx(900xx9.8xx7)/(81pixx10^5)`
`=7.8xx10^-19C`
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