Electromagnetic 3 Examination Solution 2009

Fourth Stage Electromagnetic Time: 60 minutes

Sulaimani University College of Sciences Physics Department Q1/ If

/

,

in free space, find volume charge density , .

at pointe

Q2/ A point charge is located at point , , between two semiinfinite conducting plates intersecting at right as in figure. Determine the potential at point , , and the force on Q3/ A rectangular pipe, running parallel to the z-axis ∞ metal sides, at , and . The fourth side, at potential . Find the potential within the pipe. z

∞ , has three grounded is maintained at a constant

y P(x,y,z) Q

a

b

b 90

V=V0 V=0

V=0 x

x V=0

a

Spherical Coordinate:

Cylindrical Coordinate:

Q4/ The potential is specified on the surface of a sphere of radius . Find the potential outside, assuming there is no charge there.

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Sulaimani University - College of Sciences - Physics Department Solution of Third Examination (12/2/2009) Electromagnetic Q1/ If

/ ,

in free space, find volume charge density , . /

Using Poisson’s equation in free space,

Substituting:

At Pointe

,

, . ,

at pointe

Q2/ A point charge is located at point , , between two semiinfinite conducting plates intersecting at right as in figure. Determine the potential at point , , and the force on . z P(x,y,z) Q

a b 90

x

Where:

/

/

/

Q3/ A rectangular pipe, running parallel to the z-axis ∞ ∞ , has three grounded metal sides, at , and . The fourth side, at is maintained at a constant potential . Find the potential within the pipe. y

0 Boundary conditions: 1 0 2 0 3 0 4

0

b

x V=0

, 0

Condition (1): Condition (2):

0

Condition (3): 2

sin

,

sin

Condition (4): sin Multiplied by sin sinh

2

: sin

sinh

sin 1

2 1

cos

sinh 4 sinh ,

4

V=0

V=0

0

The general solution was:

,

V=V0

sin sinh

cos

a

Q4/ The potential is specified on the surface of a sphere of radius . Find the potential outside, assuming there is no charge there. In general: , In this case:

0

. .

0

∞

, At the surface of the sphere we require that; , and integrating:

Multiplying by 2 2

1

2

1 2

Since

2 0 0 0 1 2

& and then: ,

0 1 2 3

2 0