A plastic rod with linear charge density ? is bent into the quarter circle shown

Question

A plastic rod with linear charge density ? is bent into the quarter circle shown in the figure(Figure 1) . We want to find the electric field at the origin.

1-Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle ?, with the arc length R?? .

Express your answer in terms of the variables R, ?, ?, ??, and appropriate constants.

2-

Evaluate the integrals and write E? net in component form.

Express your answer in terms of the variables R, ?, unit vectors i^, j^ and appropriate constants.

Explanation / Answer

a. Elementary charge dq due to a small section of this rod can be expressed as lambda*R*d(theta). Radial component of electric field at the origin due to this elementary charge is dE = dq/R.
X and Y components can be expressed from this using trig functions

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