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A plane square sheet of charge of side 0...

A plane square sheet of charge of side 0.5 m has uniform surface charge density. An electron at 1 cm from the centre of the sheet experiences a force of `1.6 xx 10^(-12)` N directed away from the sheet. The total charge on the plane square sheet is `(epsi _(0) = 8.854 xx 10 ^(-12) C ^(2) m ^(-2) N ^(-1))`

A

`16.25 mu C`

B

`-22.15 mu C`

C

`-44.27 mu C`

D

`144.27muC`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `l 0. 5 m `

`F = 1.6 xx 10 ^(-12) N`
`q = - 1.6 xx 10 ^(-10)C` (for electron)
`epsi _(0) = 8.854 xx 10 ^(-12) C ^(2) m ^(-2) N ^(-1)`
Electric field `E = (F)/(q)`
`or F = qE " "...(i)`
Electric field due to a square plane sheet of charge
`E = ( sigma )/( 2 epsi _(0))`
where `sigma =` surface charge density
`epsi _(0) =` permitivity of free space
Putting the value of E in Eq. (i), we get
`F =q . (sigma )/( 2 epsi _(0))`
`sigma = 2 epsi _(0) . (F)/(q)`
` sigma = ( 2 xx 8.854 xx 10 ^(-12) xx 1. 6 xx 10 ^(-12))/(-1.6 xx 10 ^(-19))`
`sigma =- 17.708 xx 10 ^(-5)`
`sigma A = l ^(2) xx (-17.708 xx 10 ^(-5))`
`= 0.5 xx 0.5 xx (- 17.708 xx 10 ^(-5))`
`= - 4.427 xx 10 ^(-5)`
`= - 44.27 xx 10 ^(-6) C`
`=- 44. 27 mu C`
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