{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Week 9 Solns

Week 9 Solns - Electromagnetics Workshop Week 9 Solutions...

This preview shows pages 1–4. Sign up to view the full content.

Electromagnetics Workshop – Week 9 Solutions Electrostatic Potential, Dielectrics, & Faraday’s Law 1 Problem 1: A regular hexagon of charge with line charge density ρ A exists in the x-y plane centered around the origin. The hexagon is inscribed within a circle of radius a . a) Find the potential due to this charge distribution along the z-axis assuming the reference is at infinity where the potential is zero. b) Repeat a assuming the reference is at the origin where the potential is 5 [V]. Since the hexagon is regular, it can be split up into six equilateral triangles. Hence, the sides of the triangles are of length a . The height of each triangle is 3 2 a . Since the charge density is uniform we can deduce that the electric field (and hence the potential) will be equally affected by each of the six sides of the hexagon. Hence, using superposition () 2 2 2 2 0 2 6 4 32 a a dy z ay z πε Φ= ++ A [] 22 0 ln V 2 2 aa z z z ⎡⎤ ⎢⎥ −+ + ⎣⎦ A 00 33 0l n 3 5 5 l n 3 CC + =⇒ = AA ( ) 0 ln 5 V 2 z z z + + A x y a A

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Electromagnetics Workshop – Week 9 Solutions Electrostatic Potential, Dielectrics, & Faraday’s Law 2 Problem 2: A hollow cylinder of surface charge 22 sin C/m s ρφ = is centered at the origin. Find the potential due to this cylinder along the z-axis. Assume ( ) 0 Φ∞= . Validate this assumption by evaluating your answer in the limit as z →∞ . () 2 2 2 2 2 0 20 sin 4 h h ad d z z az z π φφ πε ′′ Φ= +− ∫∫ 2 2 2 0 2 4 h h z z z ε [] 2 2 2 2 0 ln V 4 zh a a z a ⎡⎤ ++ + + ⎢⎥ −+ + ⎣⎦ 2 2 2 2 0 lim lim 1l n 1 0 4 a a z zz a + + =⇒ Φ = = + x y z h s ρ a
Electromagnetics Workshop – Week 9 Solutions Electrostatic Potential, Dielectrics, & Faraday’s Law 3 Problem 3: An infinitely long cylindrical shell of uniform charge density 0 s ρ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

Week 9 Solns - Electromagnetics Workshop Week 9 Solutions...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online