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1. Homework Statement
A detector hjaving a radius 10 cm is placed 1 m away from an electric dipole. What fraction of total solid angle does the detector cover and what fraction of total dipole power does it detect (assuming 100% detection efficiency)
2. The attempt at a solution
I drew the diagram as well maybe that will help. In any case, i think the detector will make a cone (?) with the dipole.Since the base of this triangle has radius of 0.1 m and the height of the triangle is 1m, the apex angle is 5.7 degrees or [itex] 57\pi/180 [/itex]
the total angle swept by the triangle is thus
[tex] \int_{0}^{2\pi}\int_{0}^{5.7\pi/180}\sin\theta\ d \theta d\phi = \frac{5.7\pi}{90}[/tex]
the total angle swept by a sphere is 4pi so the fraction is simply the answer above divided by 4pi. Is that correct?
A detector hjaving a radius 10 cm is placed 1 m away from an electric dipole. What fraction of total solid angle does the detector cover and what fraction of total dipole power does it detect (assuming 100% detection efficiency)
2. The attempt at a solution
I drew the diagram as well maybe that will help. In any case, i think the detector will make a cone (?) with the dipole.Since the base of this triangle has radius of 0.1 m and the height of the triangle is 1m, the apex angle is 5.7 degrees or [itex] 57\pi/180 [/itex]
the total angle swept by the triangle is thus
[tex] \int_{0}^{2\pi}\int_{0}^{5.7\pi/180}\sin\theta\ d \theta d\phi = \frac{5.7\pi}{90}[/tex]
the total angle swept by a sphere is 4pi so the fraction is simply the answer above divided by 4pi. Is that correct?
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