The summaries at the end of each of Topic Notes 9 to 14 are a good guide on what you should know.
You may be asked to perform the integrations involved in Gauss’ Law and Ampere’s Law for “simple” geometries.
You should be able to:
• Sketch a picture of a field using flux lines (and equipotentials for electric fields), including illustrating the concept of a flux tube. • Apply Gauss’ Law to the ideal: point charge; line charge; and parallel plate capacitor. • Determine D, E, qf , Q, C and V for simple geometrical arrangements of conductors.
• Apply Ampere’s Law to the ideal: infinitely long conductor; toroid; solenoid.
• Determine B, H, (13 , A , L and I for simple geometrical arrangements of conductors and magnetic material.
QUESTION 1
2 marks (a) State Gauss’ Law and illustrate it by a simple example.
(b) A cylindrical co-axial cable has an inner conductor of radius a and an outer conductor of radius b. The space between the conductors is filled with a dielectric of relative permittivity er =1.
Assume a uniform charge density of A, Cnil on the inner conductor. Assume the cable is so long that end effects can be neglected. 2 marks (i) Sketch the electric field distribution in the space between the conductors.
2 marks (ii) Use Gauss’ Law to find an expression for the electric flux density (D) and electric field intensity (E) at a radius r between a and b.
2 marks (iii) Find an expression for the capacitance per unit length of cable, and explain your reasoning.
2 marks
(iv) How would flux density, field intensity, and capacitance be affected if the space between the conductors were filled with a dielectric of relative permittivity er =2?
QUESTION 2
2 marks (a) State Gauss’ Law and illustrate it by a simple example.
(b) A cylindrical co-axial cable has an inner conductor of radius a and an outer conductor of radius b. The space between the conductors is filled with a dielectric of relative permittivity er =1.
Assume a uniform charge density of A, Cnil on the inner conductor. Assume the cable is so long that end effects can be neglected. 2 marks (i) Sketch the electric field distribution in the space between the conductors.
2 marks (ii) Use Gauss’ Law to find an expression for the electric flux density (D) and electric field intensity (E) at a radius r between a and b.
2 marks (iii) Find an expression for the capacitance per unit length of cable, and explain your reasoning.
2 marks
(iv) How would flux density, field intensity, and capacitance be affected if the space between the conductors were filled with a dielectric of relative permittivity er =2?
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