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A Charged particle of mass 1.0 g is susp...

A Charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizantal electric field of `4.0 xx 10 ^4 NC ^(-1)` . If the particle stays aty a distance of 24 cm from the wall in equilibrium, find the charge on the particle.

Text Solution

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Mass of the particle m `= 10^-3` kg
Length of a silk thread OA = 40 cm = 0.4 m,
Electric field `E = 4xx10^4` N/C
Distance AB = 0.24 m
In equilibrium,
`F = Tsintheta` …(1)
`mg = T costheta` ...(2)
Dividing equation (1) by (2) we get
`F/(mg)=(Tsintheta)/(Tcontheta)= tantheta`
`F = mg tan theta`
`qE = mg tan theta`
`q = (mg tantheta)/E`
`(10^-3xx9.8xx3)/(4xx10^4xx4)=1.8xx10^-7C`
Charge `q = 1.8xx10^-7C`
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