Two wires AB & CD, each `1m` length, carry a total charge of `0.2` microcoulomb each and are placed as shown in figure. The ends B & C are separated 1 m distance. Determine the value of electric intensity at the point P in the vector form.Note P is the mid point of BC.

Answer

`(-820hat(i)+1990hat(j))V/m`

Explanation

`vec(E)=underset(0.5)overset(1.5)(int)(K lambda dx)/x^(2)=-Klambda[2/3-2]=lambda/(3pi in_(0))`
From the wire CD

`E_(II)=(K lambda)/(r)(cos theta_(2)-cos theta_(1))` and
`{theta_(2)=0, theta_(1)=tan^(-12) & E_(bot)=(Klambda)/r [sin theta_(2)+sin theta_(1)]`