A thin rod bent into the shape of an arc of a circle of

radius $R$ carries a uniform charge per unit length $.$

The arc subtends a total angle $2{}_0,$ symmetric about

the $x$ axis, as shown in the figure $($Figure $1).$

Figure

Determine the magnitude of the electric field vec$(E)$ at the origin $0.$

Express your answer in terms of the variables $,{}_0,R,$ and appropriate constants.

$E=$

Part B

Determine the direction of the electric field vec$(E)$ at the origin $0.$

to the left

to the right

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