Download 1 Electric field of a discrete charge distribution (4 points) 2 Electric

PHYSICS II: EXERCISES
J. Faist
1
Series 02
due Wednesday 9.03.2011 in the exercise class (15:45)
Electric field of a discrete charge distribution (4 points)
Let us consider three identical charges q1 = q2 = q3 = q = 0.1 µC are placed at the corners
of an equilateral triangle of side l= 3 cm as displayed in Fig.1.
a) Which charge Q has to be placed in the center of gravity of the triangle in order for all
the charges to be in equilibrium? (2 points)
b) After you found out the expression and the value for Q, calculate the resulting electric
field in the midpoint of one of the triangle’s sides (i.e. the side connecting q1 to q2 ) (2
points)
q1
M
q3
q2
Figure 1:
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Electric field of a continuous charge distribution (4
points)
Calculate the electric fields for the following charge distributions.
a) The field (both components, Ex and Ey ) in the center of a half ring with radius R (see
Fig.2) and uniformly distributed charge Q. (2 points)
b) The field E(r) of a spherically symmetric charge distribution with total charge Q, whose
charge density is given as follows is: ρ(r) = ρ0 (1 − r/R) for r ≤ R and ρ(r) = 0 for r > R.
How big is ρ0 ? Where the electric field is maximum? (2 points)
1
Series 02
due Wednesday 9.03.2011 in the exercise class (15:45)
Figure 2:
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Motion in an uniform electric field (2 points)
An electron (charge -e=−1.602 × 10−19 C, m=9.1×10−31 kg) enters a region of a uniform
electric field E produced by two charged metallic plates as depicted in Fig.3 with a speed
v0 = 3×106 m/s. The region has a length l=0.1 m and the distance between the plates is d=2
cm. The electron enters in close proximity to the top plate. Which is the maximum value
of the electric field E for which the electron can exit the two plates? Sketch the trajectory
followed by the electron inside the region delimited by the two plates.
-----------------------------y
v0
d
x
l
++++++++++++++++
Figure 3:
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