a semi infinite line charge of linear charge density 'D' has the shape of an infinitely long straight wire whose one end is connected to three-fourth circle of radius 'R' while one of the diameters of 3/4th circle is parallel to the infinitely long straight part.What is the field at the centre of the circle.How?

electric field due to a finite linear charge is given by
Ex=2kD/r(sinƟ1+sinƟ2)
Ey=2kD/r(cosƟ2-cosƟ1)
So
For semi infinite wire
Ex=kd/r
Ey=-kd/r
And resultant will be
E=√2kD/r
(Shown in fig)
Now E due to an arc is given by
E=(2kD/r )sin(Ɵ/2)
Here Ɵ=270 degree
 
E=√2kD/r
At the center of circle,
 The direction of the electric fields is opposite with equal magnitude
So resultant will be zero

 

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