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(PHYS013)[2008](s)midterm~dli^_10536.pdf
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Midterm examination PHYS013 (100 points = 100, Full grade)
Attentions:
(1) Detail steps should be given in your answers! Grades are given according to steps.

(2) Make clear drawings to express your thoughts when necessary.

(3) Hand writing should be clear and
recognizable.



1. (25 points) Two identical dipoles (each consists of two opposite charges +q and Cq separated by s, the dipole momentp=2qs) are separated by a distance of r (center to center), asshown below.

(a) Write an expression for the net force exerted between the two dipoles

(b)Is this force attractive or repulsive?

(c) Use the binomial approximation (1+x)-n1-nx if x<<1 to approximate your result for r>>s in terms of p and r.


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(d)Rotate the right dipole by 90, 180, 270, repeat (b) and
(c)

(e) Repeat (b) and (c) when the two dipoles are parallel and anti-parallel.

(f) Discuss which configuration gives the weakest force and which configuration gives the strongest force.


2. (25 points) A problem of practical interest is to make a
beam of electrons turn a 90 angle. This can be done with theparallel-plate capacitor shown below.

An electron with kinetic energy 3.010-17 J moves up, at 45 angle, through a small hole in the bottom plate of the capacitor.
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(a) Should the bottom plate be charged positive or negative relative to the top plate to make the electron turn to right?

(b) What strength electric field is needed if the electron is to emerge from an exit hole 1.0 cm away from the entrance hole,traveling at right angle to its original direction? Hint: choosethe x, y vectors shown in the figure.

(c) What minimum separation d must the capacitor plates
have?


(d) Calculate the kinetic energy of the exit electron.

(e) If the angle is changed from 45 to 30, what is the anglebetween the enter path and the exit path of the electron.Repeat (b) to (d)?

(f) Use your results to design an instrument to measure m/q of charged particles. Describe its working principle.


3.

(20 points) Two very large slabs of metal are parallel at distanceL apart. Each slab has a total surface area (top + bottom) A. The
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thickness of each slab is so small in comparison to its lateraldimensions that the surface area around the sides is negligible.The up slab has total charge Q and the bottom slab has totalcharge 2Q. Assume Q is positive. In term of Q and A, determine:
(a) The electric field strength E1 to E5 in regions 1 to 5.

(b) The surface charge density to d on the four surfaces a


a
to d.
4.

(15 points) A wire is made of two equal-diameter segments with conductivity 1 and 2. When current I passes