A thread carrying a uniform charge λ per unit length has the configuration shown in figure a and b. Assuming a curvature radius r to be considerably less than the length of the thread, find the magnitude of the electric field strength at the point O.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
E = 
E = 0
Sol.
here 
= field due to wire 1 (Infinitely long)
= field due to wire 2
= field due to wire 3
So, Net Electric field:
= 
+ 
+ 
= – 
∴ 
= 
= 
= 
Also here,
= Electric field due to wire 1.
= Electric field due to wire 2.
= Electric field due to wire 3 (Ring).
= 
+ 
+ 
In X axis: E 1 cos 45 o – E 2 cos 45 o = 0 {E 1 = E 2 }
In Y axis: E 1 sin 45 o + E 2 sin 45 o – 
= 
+ 
– 
= 0
⇒ Electric field at center = 0
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