Imperfect Symmetry

Electricity and Magnetism Level 4

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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