A 3-D printer lays down a semicircular arc of positively charged plastic with a radius R = 2.8 cm, and a linear charge density of λ = +1.6 μC/m. After the printer has finished the arc, the stylus moves to the center of the arc as shown. The minute segment of the plastic arc highlighted in the diagram subtends an angle dθ. 1. Input an expression for the charge dq on the segment of size dθ in terms of given parameters. 2. Input an expression for the electric field vector, dE, generated at the center of the arc by the minute segment of plastic subtending the arc dθ. Express your answer in terms of given parameters, the Coulomb constant k, and the unit vectors i and j. 3. Evaluate the expression from part (b) as an indefinite integral to determine the x-component of the electrical field, Ex, at the center of the arc generated by the entire line of charged plastic.
A 3-D printer lays down a semicircular arc of positively charged plastic with a radius R = 2.8 cm, and a linear charge density of λ = +1.6 μC/m. After the printer has finished the arc, the stylus moves to the center of the arc as shown. The minute segment of the plastic arc highlighted in the diagram subtends an angle dθ.
1. Input an expression for the charge dq on the segment of size dθ in terms of given parameters.
2. Input an expression for the electric field vector, dE, generated at the center of the arc by the minute segment of plastic subtending the arc dθ. Express your answer in terms of given parameters, the Coulomb constant k, and the unit vectors i and j.
3. Evaluate the expression from part (b) as an indefinite integral to determine the x-component of the electrical field, Ex, at the center of the arc generated by the entire line of charged plastic.
4. Select the limits of integration that would result in the correct calculation of the electric field at the center of the arc generated by the entire line of charged plastic as shown in the diagram.
5. Use the limits from part (d) and the expression from part (c) to determine an expression for the magnitude of the electric field at the center of the arc generated by the entire line of charged plastic.
6. Calculate the magnitude of the electric field (in N/C) at the center of the arc generated by the entire line of charged plastic.
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