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Direction of vector of electric field

Suppose we have a arc of charges with some charge density $\lambda(\theta) = sin\theta$.I am using polar coordinates for convenience.But how can I find the direction of the unit vector of the net electric field?In the previous example (the one with the line of charges)the direction of the net electric field is easily found because we only have charges in the x axis.However what happens now that I use polar coordinates?Shouldnt it just be $\vec{r}$ but i am cconfused because it is counter intuitive if the unit vector is in the $\vec{r}$ direction then it could be any vector pointing outwards from point A.So what is going on here?
![](https://physics.codidact.com/uploads/GGP3wjrn6C2LQXZYY1ssQdQq)

Suppose we have a arc of charges with some charge density $\lambda(\theta) = sin\theta$.I am using polar coordinates for convenience.But how can I find the direction of the unit vector of the net electric field?In the previous example (the one with the line of charges)the direction of the net electric field is easily found because we only have charges in the x axis.However what happens now that I use polar coordinates?Shouldnt it just be $\vec{r}$ but i am cconfused because it is counter intuitive if the unit vector is in the $\vec{r}$ direction then it could be any vector pointing outwards from point A. So what is going on here?
![](https://physics.codidact.com/uploads/GGP3wjrn6C2LQXZYY1ssQdQq)

electrostatics vectors differential-calculus charge-density