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# T07test mac - ELECTROMAGNETIC THEORY TUTORIAL 7 PRACTICE...

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1 ELECTROMAGNETIC THEORY TUTORIAL 7: PRACTICE TEST Tutorial Classes: This is a practice test not for assessment. Please use vector notation where appropriate. Time: 45 minutes. Answer ALL of the following. 1. (5 marks) (a) Explain the Principle of Superposition as it applies to the electric force produced by two point charges at a distant point in space. (b) Write the Lorentz force Law and comment on its relationship to the Principle of Superposition (that is, how it extends the Principle of Superposition). 2. (4 marks) (a) Define in words the flux of a vector field A . (b) If A is a velocity, what does the flux represent? (c) Sketch the field due to a point charge and sketch two closed surfaces, one with zero flux and one with non-zero flux.

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2 3. (2 marks) (a) Define in words the circulation of a vector field B . (b) If B is a velocity, what does the circulation represent? 4. (7 marks) (a) Write the most general expression for the electric flux density in a medium, defining all terms. (b) Describe the underlying model used to obtain the expression in (a). (c) Write the most general integral form of Gauss’s Law that holds in any medium. (d) Write the integral form of Gauss’s Law in an LIH medium in terms of the electric field intensity. Define precisely what is meant by the symbol ! v on the right hand side of the equation.
3 5. (3 marks) (a) Define the divergence of a vector field A in terms of flux. (b) Write the most general point (differential) form of Gauss’s Law that holds in any medium. 6. (8 marks) (a) Why are equipotential surfaces of an electrostatic field perpendicular to the flux lines? Use this fact to derive a boundary condition between a conducting and an insulating medium. (b) Explain what is meant by the following: “The electrostatic field is not what makes circuits work.” (c) Explain why there is a negative sign in the definition of potential. 7. (4 marks) Capacitor A has twice the mean square field strength, one quarter the dielectric constant, and three times the dielectric volume of capacitor B. Which capacitor stores the most energy, and by how much?

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4 8. (5 marks) (a) Write Ohm’s Law in point form and state the most important assumption upon which it depends. (b) Write Laplace’s equation. Under what circumstances is it useful? 9. (12 marks)
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T07test mac - ELECTROMAGNETIC THEORY TUTORIAL 7 PRACTICE...

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