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(B) The upper half of the ring has a positive linear charge density $\lambda$. The electric field at the centre $O$ due to this positive charge will b

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along $OB$

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(B) The upper half of the ring has a positive linear charge density $\lambda$. The electric field at the centre $O$ due to this positive charge will be directed away from the arc,i.e.,towards the bottom-right direction.The lower half of the ring has a negative linear charge density $-\lambda$. The electric field at the centre $O$ due to this negative charge will be directed towards the arc,i.e.,also towards the bottom-right direction.By symmetry,the horizontal components of the electric fields from both halves cancel out,while the vertical components add up in the downward direction. However,looking at the geometry of the arc placed on the left of the centre $O$,the net electric field vector points towards the right,specifically along the direction $OB$.

The linear charge density on the upper half of a segment of a ring is $\lambda$ and on the lower half,it is $-\lambda$. The direction of the electric field at the centre $O$ of the ring is:

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