Problem 11.4A rotating electric dipole can be thought of as the superposition of two oscillating dipoles, one along the x axis and the other along the y axis (Fig. 11.7), with the latter out of phase by 90°: p = Polcos(ot) â& + sin(@t) §]. +q FIGURE 11.7 Using the principle of superposition and Eqs. 11.18 and 11.19 (perhaps in the form suggested by Prob. 11.2), find the fields of a rotating dipole. Also find the Poynting vector and the intensity of the radiation. Sketch the intensity profile as a function of the polar angle 0, and calculate the total power radiated. Does the answer seem reasonable? (Note that power, being quadratic in the fields, does not satisfy the superposition principle. In this instance, however, it seems to. How do you account for this?)
Problem 11.4A rotating electric dipole can be thought of as the superposition of two oscillating dipoles, one along the x axis and the other along the y axis (Fig. 11.7), with the latter out of phase by 90°: p = Polcos(ot) â& + sin(@t) §]. +q FIGURE 11.7 Using the principle of superposition and Eqs. 11.18 and 11.19 (perhaps in the form suggested by Prob. 11.2), find the fields of a rotating dipole. Also find the Poynting vector and the intensity of the radiation. Sketch the intensity profile as a function of the polar angle 0, and calculate the total power radiated. Does the answer seem reasonable? (Note that power, being quadratic in the fields, does not satisfy the superposition principle. In this instance, however, it seems to. How do you account for this?)
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![III. PROBLEM 3. ELECTRIC DIPOLE RADIATION.
Problem 11.4A rotating electric dipole can be thought of as the superposition
of two oscillating dipoles, one along the x axis and the other along the y axis
(Fig. 11.7), with the latter out of phase by 90°:
p = Po[cos(ot) â& + sin(@t) ŷ].
+q
FIGURE 11.7
Using the principle of superposition and Eqs. 11.18 and 11.19 (perhaps in the form
suggested by Prob. 11.2), find the fields of a rotating dipole. Also find the Poynting
vector and the intensity of the radiation. Sketch the intensity profile as a function
of the polar angle 0, and calculate the total power radiated. Does the answer seem
reasonable? (Note that power, being quadratic in the fields, does not satisfy the
superposition principle. In this instance, however, it seems to. How do you account
for this?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ecaf638-5b80-48e0-b315-f5c22540f226%2F2edbb986-9206-4927-87bc-d2fc918530c6%2Ft7xkl9_processed.png&w=3840&q=75)
Transcribed Image Text:III. PROBLEM 3. ELECTRIC DIPOLE RADIATION.
Problem 11.4A rotating electric dipole can be thought of as the superposition
of two oscillating dipoles, one along the x axis and the other along the y axis
(Fig. 11.7), with the latter out of phase by 90°:
p = Po[cos(ot) â& + sin(@t) ŷ].
+q
FIGURE 11.7
Using the principle of superposition and Eqs. 11.18 and 11.19 (perhaps in the form
suggested by Prob. 11.2), find the fields of a rotating dipole. Also find the Poynting
vector and the intensity of the radiation. Sketch the intensity profile as a function
of the polar angle 0, and calculate the total power radiated. Does the answer seem
reasonable? (Note that power, being quadratic in the fields, does not satisfy the
superposition principle. In this instance, however, it seems to. How do you account
for this?)
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