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Two electrons are held at some separatio...

Two electrons are held at some separation. A third charge q is to be placed at the midpoint between these two electrons. What should q be so that electric potential energy of the system becomes zero?

Text Solution

Verified by Experts

The given arrangement of charges is shown below:

Here `q_(e)=` Magnitude of charge on an electron The potential energy of the system is zero.
`therefore U=(1)/(4pi epsilon_(0))[((-q_(e))q)/(r )+(q(-q_(e)))/(r )+((-q_(e))(-q_(e)))/(2r)]=0`
`rArr -q q_(e)-q q_(e)+(q_(e)^(2))/(2)=0`
`rArr -2q q_(e)= -(q_(e)^(2))/(2)`
`rArr 4q=q_(e )`
`rArr q=q_(e)//4`
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