PHYS225/PHY8225 – Assignment 3, 2019

Set on Thu 26th September, due on Mon 14th October.

MATLAB

For a full mark, the student is asked to answer 4 questions correctly and for each of them, he/she must:

- To submit BY EMAIL all .m files collected into ONE SINGLE .ZIP file to jeremyd@uow.edu.au.

- Each .m file must run on MATLAB without errors or warnings.

- To complete the question on all its parts (derivation, calculations and MATLAB code);

- Derivation and calculations must be submitted along with the plot or plots showing the output of the MATLAB code to EIS with a coversheet.

- To summarise: o Material to be submitted through EIS FOR EACH QUESTION is:

? The code typed

? The plots produced by the code

? The derivation or calculations required to write the code or to answer to the questions.

Question 1

Using MATLAB/OCTAVE, plot the vector field

??? = ??2??^ - ????^ ???? ??h?? ???????????? - 2 ?? +2 ?????? - 2 ?? +2

Find the magnitude of the vector field at the point (??0, ??0) = (3,2).

Question 2

Derive the magnetic field B inside and outside of an infinite thick wire with radius a=1. The wire carries a uniformly distributed current I=1A in the direction outwards the page.

Plot the magnetic flux density in the region -2 x +2 and -2 y +2 that is internal to the wire and external to the wire. The expected result should look like Fig.1

Fig.1

Question 3

Using MATLAB/OCTAVE and the Method of Moments (MoM), find the charge distribution on a cylindrical conductor whose radius is a=0.01m and length L=1m. The potential on the wire is V=1V. You may assume that the charge is distributed uniformly within each section. Assume that the number of the sections is N=5 and the step size is ?L=0.2m.

Question 4

For the indicated boundary conditions that are specified in the figure, derive analytically the electric potential distribution V(x,y) within the enclosed region by solving Laplace’s equation (Hint: by separation of variables). Plot the potential distribution using FDM with:

- a=1 m

- V0=25 V

y

a

V=0

V0

Compare and comment the results obtained using the analytical solution and the FD method.

Set on Thu 26th September, due on Mon 14th October.

MATLAB

For a full mark, the student is asked to answer 4 questions correctly and for each of them, he/she must:

- To submit BY EMAIL all .m files collected into ONE SINGLE .ZIP file to jeremyd@uow.edu.au.

- Each .m file must run on MATLAB without errors or warnings.

- To complete the question on all its parts (derivation, calculations and MATLAB code);

- Derivation and calculations must be submitted along with the plot or plots showing the output of the MATLAB code to EIS with a coversheet.

- To summarise: o Material to be submitted through EIS FOR EACH QUESTION is:

? The code typed

? The plots produced by the code

? The derivation or calculations required to write the code or to answer to the questions.

Question 1

Using MATLAB/OCTAVE, plot the vector field

??? = ??2??^ - ????^ ???? ??h?? ???????????? - 2 ?? +2 ?????? - 2 ?? +2

Find the magnitude of the vector field at the point (??0, ??0) = (3,2).

Question 2

Derive the magnetic field B inside and outside of an infinite thick wire with radius a=1. The wire carries a uniformly distributed current I=1A in the direction outwards the page.

Plot the magnetic flux density in the region -2 x +2 and -2 y +2 that is internal to the wire and external to the wire. The expected result should look like Fig.1

Fig.1

Question 3

Using MATLAB/OCTAVE and the Method of Moments (MoM), find the charge distribution on a cylindrical conductor whose radius is a=0.01m and length L=1m. The potential on the wire is V=1V. You may assume that the charge is distributed uniformly within each section. Assume that the number of the sections is N=5 and the step size is ?L=0.2m.

Question 4

For the indicated boundary conditions that are specified in the figure, derive analytically the electric potential distribution V(x,y) within the enclosed region by solving Laplace’s equation (Hint: by separation of variables). Plot the potential distribution using FDM with:

- a=1 m

- V0=25 V

y

a

V=0

V0

Compare and comment the results obtained using the analytical solution and the FD method.

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