Solutions: Mid semester exam 2014 - edX · Solutions: Mid semester exam 2014 Q1 PART A Cartesian:...
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Solutions: Mid semester exam 2014 Q1 PART A Cartesian: ∇ = 2 ! + Cylindrical: ∇ = 2 ! Q1 PART B 2 + 2 Q1 PART C 4 ! Q2 PART A −3 ! Q2 PART B 36 Q3 PART A = 0 < = ln ! ! < < = ln ! ! >
Transcript of Solutions: Mid semester exam 2014 - edX · Solutions: Mid semester exam 2014 Q1 PART A Cartesian:...
Solutions: Mid semester exam 2014 Q1 PART A
Cartesian: ∇𝑉 = 2𝑉! 𝑥𝐱+ 𝑦𝐲
Cylindrical: ∇𝑉 = 2𝑉!𝑠𝐬 Q1 PART B
𝛼2 +
2𝛽
Q1 PART C
4𝛼𝜋𝑅! Q2 PART A
−3𝜋𝑅! Q2 PART B
36𝜋 Q3 PART A
𝐄 = 0 𝑟 < 𝑎
𝐄 =𝑘 ln 𝑟𝑎𝑟!𝜀!
𝐫 𝑎 < 𝑟 < 𝑏
𝐄 =𝑘 ln 𝑏𝑎𝑟!𝜀!
𝐫 𝑟 > 𝑏
Q3 PART B
𝐄 =−𝐴𝑎!
4𝜀!
1𝑧! + 𝑎! !/! 𝐲
Q3 PART C
𝐄 =𝛼4𝜀!
𝑠!𝑧
𝑧! + 𝑠! !/!
!
!𝑑𝑠𝐳
𝑉 =𝛼4𝜀!
𝑠!𝑧
𝑧! + 𝑠! !/!
!
!𝑑𝑠
