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A positive point charge q(1) is placed a...

A positive point charge `q_(1)` is placed at `(a,0)` and another positive point charge `q_(2)` is placed at (0,a) . Find the force acting on `q_(1)`.

Text Solution

Verified by Experts

As shown, the separation between the charges is a `sqrt(2)`.
The magnitude of force acting on `q_(1)` is
`F= ((1)/(4piepsilon_(0)))(q_(1)q_(2))/((asqrt(2))^(2))= (1)/(4pi epsilon_(0))(q_(1)q_(2))/((2a^(2)))`
Also, `tan theta= (a)/(a) = 1 implies theta = 45^(@)`
` :. bar(F) =F costheta vec(l)-Fsin thetavec(j) = (1)/( 4pi epsilon_(0))(q_(1)q_(2))/(2a^(2))((1)/(sqrt(2))vec(i)(-1)/(sqrt(j))vec(j))=(1)/(4piepsilon_(0))(q_(1)q_(2))/(2a^(2))((1)/(sqrt(2))vec(i)-(1)/(sqrt(2))vec(j))`
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