How could I find the total electric field in this question?

[Gnall]

Homework Statement

Hello. There is a semicircle charged ring and I found the electric field at the origin. But there is an also extra charge near the origin and the total electric field is zero. I need the charge. I'm trying to solve the 1-b question in the image.

Relevant Equations

Electric field.

The electric field due to the semicircle is 2kQ/pi.Rsquare
Sorry for the bad english.

 

[haruspex]

The electric field due to the semicircle is 2kQ/pi.Rsquare
Sorry for the bad english.

Having solved a, b looks rather straightforward.
Please post an attempt as per forum rules.

 

[Gnall]

I found that. Is that true?

 

[Gnall]

Having solved a, b looks rather straightforward.
Please post an attempt as per forum rules.

Kq/aSquare=2kQ/piRsquare,
So q=2QaSquare/piRsquare
Is that true?

 

[Aryamaan Thakur]

You already found the electric field at centre due to semicircular ring. Find the field due to point charge placed at distance 'a'. Check the directions and add them vectorially (basically just equate them).

P.S. You got the right answer.

 

[Gnall]

You already found the electric field at centre due to semicircular ring. Find the field due to point charge placed at distance 'a'. Check the directions and add them vectorially (basically just equate them).

P.S. You got the right answer.

Thank you so much :)