Electromagnetic 2 Examination Solution 2009

Fourth Stage Electromagnetic Time: 60 minutes

Sulaimani University College of Sciences Physics Department

Q1/ A charge distribution with spherical symmetry has density , determine the energy stored in region .

everywhere and

Q2/ A total charge of is uniformly distributed over a circular ring of radius . Find the potential at a distance above the center of the disk. Q3/ Determine , at 2,0, 0 with 12 uniform line at 6 ,

due to three charge distributions as follows; a uniform sheet at / , a uniform sheet at 4 with 12 / , and a 0 with 2 / .

Q4/ Show that the energy of

charge distribution is given by:

Spherical Coordinate:

Cylindrical Coordinate:

, ,

·

·

Sulaimani University - College of Sciences - Physics Department Second Examination (21/1/2009) Electromagnetic Q1/ A charge distribution with spherical symmetry has density , determine the energy stored in region .

Outside the sphere:

Inside the sphere: · ·

. .

everywhere and

Q2/ A total charge of is uniformly distributed over a circular ring of radius . Find the potential at a distance above the center of the ring. Z

r = ρ 2 + z2

Q = λ dl

λ dl V =∫ = 4π ε o r

2π

dl = ρ dφ

λ ρ dφ λ ρ = 2 2 ρ +z 2εo ρ 2 + z2 o

∫ 4π ε 0

Q Q = λ dl = λ ( 2 π ρ ) ⇒ λ ρ = 2π Q ∴V = 4π ε o ρ 2 + z 2

Q3/ Determine , at 2,0, 0 with 12 uniform line at 6 ,

(0, Φ,z)

r + + + + ++ + + ρ + + + + + (ρ+,Φ,0)

due to three charge distributions as follows; a uniform sheet at / , a uniform sheet at 4 with 12 / , and a 0 with 2 / .

, ,

.

/

Q4/ Show that the energy of

charge distribution is given by: