Electromagnetism Question

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3. A semicircular charged line of radius a carries uniform linear charge density 2. The semicircle is in the xy plane with center at the origin as shown in the figure below. Find the electric field at a point P on the z axis a distance z from the origin. a х a -a P. Z
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Explanation & Answer

Here's the solution in doc and pdf format.Let me know if you have any issues.

b

r

𝜃

𝐸⃗𝑦

𝐸⃗𝑧

𝐸⃗

Based on symmetry, this arrangement will provide an electric field in both the y and z directions.
Using the geometry I’ve outlined (sorry for the sloppiness)
z is the distance from the origin to P (I guess you could just use P, sub this in at the end or leave it as z)
r is the distance from P to any point on the semi-...


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