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?

E

_{x}=2kD/r(sinƟ

_{1}+sinƟ

_{2})

E

_{y}=2kD/r(cosƟ

_{2}-cosƟ

_{1})

So

For semi infinite wire

E

_{x}=kd/r

E

_{y}=-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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