Cylindrical and rectangular components.

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Question 1

a) Express the field 𝑫 = (𝑥2 + 𝑦2)−1(𝑥𝒂𝑥 + 𝑦𝒂𝑦) in cylindrical components and cylindrical variables.
b) Evaluate 𝑫 at the point where 𝜌 = 2, 𝜙 = 0.2𝜋, and 𝑧 = 5, expressing the result in cylindrical and rectangular components.

 
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Question 2

A uniform line charge of 16 nC/m is located along the line defined by 𝑦 = −2, 𝑧 = 5. a) Find 𝑬 at 𝑃(1,2,3)
b) Find 𝑬 at that point in the 𝑧 = 0 plane where the direction of 𝑬 is given by (1/3)𝒂𝑦 − (2/3)𝒂𝒛.

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Question 3

The cylindrical surface 𝜌 = 8 cm contains the surface charge density, 𝜌𝑆 = 5𝑒−20|𝑧| nC/m2.

a) What is the total amount of charge present?
b) How much electric flux leaves the surface 𝜌 = 8 cm, 1 cm < 𝑧 < 5 cm, 30o < 𝜙 < 90o?