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An infinite plane of positive charge has...

An infinite plane of positive charge has a surface density `sigma`. A metal ball of mass m and charge q is attached to a thread and tied to a point on the plane . Find the angle `theta` which the thread makes with the charged plane .

Text Solution

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Electric field due to a charged conduction infinite plane on this sheet of surface charge density `sigma ` is given by `E = (sigma)/(2epsi_(0))`
where `epsi_(0)` is permittivity in free space . Due to this field , the charge will experience a force , its free body diagram is shown as below .

In equilibrium
`T cos theta = mg " "`... (i)
and `T sin theta = q E " "` ... (ii)
Dividing Eq. (ii) by Eq. (i) , we get
`tan theta = (qE)/(mg)`
`implies tan theta = ((q sigma)/(2 m g epsi_(0))) implies theta = tan^(-1) ((q sigma)/(2 mg epsi_(0)))`
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