This Free Response Question includes the following concepts: Electrostatic Forces, Gauss's Law, Electric Fields and work done on a charged particle when moving through an electric potential difference.

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Link: AP Physics C 1998 Released Exam
The problem is on pages 163 - 165 of this pdf.
Their solution is on pages 200 - 201 of this pdf.
Please enjoy my solutions as well.

Content Times:
0:31 Part (a)
1:20 Part (a) The Free Body Diagram
2:51 Part (a) Summing the forces in the y-direction
3:57 Part (a) Summing the forces in the x-direction
6:36 Part (b)
7:32 Part (b) What happens to the angle?
9:38 Part (c)
10:36 Part (c) Gauss's Law
12:07 Part (c) Using Gauss's Law
14:03 Part (c) Using Linear Charge Density
15:31 Part (d)
16:38 Part (e)
17:32 Part (e) Integration