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Date: 29-8-2016
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Date: 2-8-2016
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Date: 8-8-2016
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Charge and Dielectric
A charge e is situated at the point x = h > 0, y = z = 0 outside a homogeneous dielectric which fills the region x < 0 (see Figure 1.1).
Figure 1.1
a) Write the electric fields E(0+, y, z) and E(0-, y, z) just outside and just inside the dielectric in terms of the charge e and surface charge density σb of bound charges on the surface of the dielectric.
b) Express σb in terms of E(0-, y, z). Denote by the dielectric constant of the dielectric.
c) By using the equations obtained in (a) and (b), show that
d) Calculate the electric field E' due σb to at the position (h, 0, 0) of the charge e. Show that it can be interpreted as the field of an image charge e' situated at the point (-h, 0, 0).
e) Show that the charge experiences the force
SOLUTION
a) The electric fields just above and below the dielectric due to the charge e and the surface charge σb(y, z) are, respectively,
(1)
(2)
b) From D = E + 4πP = εE, we have for the polarization P and its normal component to the boundary Pn
(3)
c) Using (2) in (3), we have
(4)
So
(5)
d) The field at the position of the charge due to the surface charge σb is
(6)
where dA is the area. We can rewrite this integral in cylindrical coordinates:
(7)
This can be interpreted as an image charge
(8)
at a distance 2h from the charge e (see Figure 1.2).
Figure 1.2
e) The force on the charge e is
(9)
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"إنقاص الوزن".. مشروب تقليدي قد يتفوق على حقن "أوزيمبيك"
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الصين تحقق اختراقا بطائرة مسيرة مزودة بالذكاء الاصطناعي
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قسم شؤون المعارف ووفد من جامعة البصرة يبحثان سبل تعزيز التعاون المشترك
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