Electricity and Magnetism

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Electric Field Due to an Asymmetric Arc of Charge

EANDM-H7JUDV

Figure 1 depicts an asymmetric arc of charge in the $x$-$y$ plane. All charges are located a distance $r = 2.6 \text{ cm}$ from the origin of coordinates.

Figure 1. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

The line of charge consists of a total charge $q = - 0.55 \; \mu\rm{C}$, extending from an angle $\theta_0 = -20^\circ$ with respect to the positive $x$-​axis to an angle $\theta_f = +60^\circ$ with respect to the positive $x$-axis.

What is the electric field at the origin due to this line of charge?

A

$\vec{E} = 6.63 \times 10^6 \hat{x} + 6.63 \times 10^6 \hat{y}$ N/C

B

$\vec{E} = 7.32 \times 10^6 \hat{x} + 7.32 \times 10^6 \hat{y}$ N/C

C

$\vec{E} = 6.87 \times 10^6 \hat{x} + 2.50 \times 10^6 \hat{y}$ N/C

D

$\vec{E} = 6.23 \times 10^6 \hat{x} + 2.27 \times 10^6 \hat{y}$ N/C