The charge configuration at the right consists of an insulating rod that is bent into the shape of a quarter-circle having total positive charge Q distributed uniformly over its length. Suppose that the magnitude of the total electric field at the origin due this charge configuration is E0.
In terms of E0, what would be the total electric field vector at the origin due to the semi-circle of charge shown below? The left quarter-circle has negative charge, -Q, distributed uniformly and the right quarter-circle has positive charge, Q, distributed uniformly.

Question

The charge configuration at the right consists of an insulating rod that is bent into the shape of a quarter-circle having total positive charge Q distributed uniformly over its length. Suppose that the magnitude of the total electric field at the origin due this charge configuration is E0.
In terms of E0, what would be the total electric field vector at the origin due to the semi-circle of charge shown below? The left quarter-circle has negative charge, -Q, distributed uniformly and the right quarter-circle has positive charge, Q, distributed uniformly.

anonymous · Answer

I would assume that the vertical direction would cancel out, so it would move in the negative x direction. But, i'm not sure how to go about doing this

anonymous · Answer

the answer is
$$-\sqrt{2}Eo$$