An infinitely long string uniformly charged with a linear charge density λ 1 and a segment of length λ uniformly charged with linear charge density λ 2 lie in a plane at right angles to each other and separated by a distance r 0 as shown in figure. The force with which these two interact is 
λ n(x). If λ = r 0 , then find the value of x.
Text Solution
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(4)
Sol. Electric field due to infinitely long charged wire at distance r from it = 
Now, we take small element dr on wire which is having distance r from wire
Now, force on this element = (λ 2 dr). 
or dF = 
Total force = 
= 
= 2kλ 1 λ 2 λ n 
= 
λ n(4) (since λ = r 0 )
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