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Physics 321 Electromagnetism I First midterm 8.20 am Wednesday 31 October

Autumn 2012 Instructor: David Cobden A102

Do not turn this page until the buzzer goes at 8.20.

Hand your exam to me before I leave the room at 9.25.

Attempt all the questions.

Please write your name on every page and your SID on the first page.

Write all your working on these question sheets. Use this front page for extra working. It is importantto show your calculation or derivation. Some marks are given for showing clear and accurate working

and reasoning.

Watch the blackboard for corrections and clarifications during the exam.

This is a closed book exam. No books, notes, or calculators allowed.

From Abstruse Goose

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1.[8] State carefully both the differential and integral forms of the relationship between the potentialand the charge density in electrostatics.

2.[8] Calculate the electric fields and charge densities associated with the following two potential

functions specified in some finite region in dimensionless Cartesian coordinates (dont worry aboutdimensions):

(i) cos (ii)

3.

[4] The electric field in the two cases is very different but not the charge density. How is this

possible?

4.[6] A long straight cylindrical metal wire of radius is held in vacuum at potential and carries a

positive charge density per unit length . What are the surface charge density and the electric field atits surface?

5.[8] Find the potential near the wire, making use of Gausss law.

6. [8] A particle of mass and positive charge is released from rest at the surface of the wire. Find

its speed when it reaches a distance from the axis of the wire.

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7. [5] Is it possible to position other charges or conductors around the wire in such a way as to trapthe particle in a region of free space? Why (not)?

8. [6] An isolated conducting sphere of radius is initially at zero potential. A positive charge isthen transferred to it. What is the increase in its potential?

9. [10] The sphere is then brought up to a distance from a grounded (at 0) infinite conductingplane. Sketch below the lines of electric field and the equipotentials in the space between and aroundthem. Also indicate the charge densities on the conductors.

10.[5] Is the potential on the sphere now higher than, lower than, or the same as when it was far away

from the conducting plane? Why?

11.[5] State the uniqueness theorem for Laplaces equation and say how it is used in the method of

images.

12.[5] Is there a simple image charge arrangement that gives the correct electric fields in question 9?

Explain.

Q

0

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13.[4] A capacitor consists of two circular parallel metal disks of radius and spacing . What

is the advantage of assuming ? Make a sketch if it helps.

14.[6] The charge on the capacitor is and the potential difference is . Find the attractive forcebetween the plates.

15.[6] Find the total energy stored in the electric field between the plates.

16.[6] The plates are moved apart until their spacing is doubled. Find the change in energy stored if is held constant.

17.[6] Find the change in energy stored if the spacing is doubled keeping instead the charge fixed.

18.[4] Why is there more energy stored in one case than the other, and where did it go to?