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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

`1.6xx10^(-19)C`

B

`3.2xx10^(-19)C`

C

`4.8xx10^(-19)C`

D

`8.0xx10^(-19)C`

Text Solution

Verified by Experts

The correct Answer is:
D
Balancing forces we have, `qE=mg` . . . (i)
`6pietarv=mg`
`(4)/(3)pir^(3)rhog=mg` . . . (ii)
`therefore r=((3mg)/(4pirhog))^(1//3)` . . . (iii)
Substituting the value of r in Eq. (ii), we get
`(qE)^(2)=((3)/(4pirhog))(6pietav)^(3)`
`therefore q=(1)/(E)((3)/(4pirhog))^(1//2)(6pietav)^(3//2)`
Substituting the values, we get
`q=(7)/(81pixx10^(5))sqrt((3)/(4pixx900xx9.8)xx216pi^(3))`
`xxsqrt((1.8xx10^(-5)xx2xx10^(-3))^(3))=8.0xx10^(-19)C`
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Knowledge Check

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    B
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