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Solutions: Mid semester exam 2015 Q1 PART A
Zero for both sides Q1 PART B
3154 𝜋
Q2 PART A
𝐄 =1
4𝜋𝜀!
−2𝐿𝑧! + 𝐿! !/! + ln
𝐿 + 𝑧! + 𝐿! !/!
−𝐿 + 𝑧! + 𝐿! !/! 𝐱
𝑉 = 0 Q2 PART B
𝐄 = −𝑎 𝛼 + 𝛽
4𝜀!𝑧! 𝑧! + 𝑎! !/! 𝐱+ 𝐲
𝑉 = 0 Q3 PART A
𝐅 = −131𝑞!
48 4𝜋𝜀!𝑑! 𝐳
Q3 PART B
𝐅 = −𝑞
4𝜋𝜀! 3𝑟! 𝐫−
𝑑𝑟! 2 cos𝜃 𝐫+ sin𝜃 𝛉
Q3 PART C
815𝛼𝛽 +
34𝛽
𝐄 = 0 𝑟 < 𝑎
𝐄 =𝑘 ln 𝑟𝑎𝑟!𝜀!
𝐫 𝑎 < 𝑟 < 𝑏
𝐄 =𝑘 ln 𝑏𝑎𝑟!𝜀!
𝐫 𝑟 > 𝑏
Q4 PART A
𝐄 = 0 𝑟 < 𝑎
𝐄 =𝑘 ln 𝑟𝑎𝑟!𝜀!
𝐫 𝑎 < 𝑟 < 𝑏
𝐄 =𝑘 ln 𝑏𝑎𝑟!𝜀!
𝐫 𝑟 > 𝑏
Q4 PART B
𝐄 = −𝑘𝑟!
𝜀! 𝐫
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