Imperfect Symmetry

Charge is unevenly distributed over a unit circle centered on the origin $$(0,0)$$. The linear charge density is $$\sigma=\sin(\theta)$$.

The magnitude of the electric field at the origin can be expressed as $$\alpha$$$$k$$, where $$k$$ is the Coulomb constant. Enter the value of $$\alpha$$, given to two decimal places.

Details and Assumptions:

Assume standard SI units for all quantities.

Note that $$\sin(\theta)$$ is negative for some values of $$\theta$$.

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