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# (Solved): An antenna is created by wrapping a square frame of side length $$a$$ by a wire $$N$$ times and ...

An antenna is created by wrapping a square frame of side length $$a$$ by a wire $$N$$ times and then connecting leads to resistor $$R$$ and capacitor $$C$$ as shown in figure. The loop itself has self-inductance L. Plane electromagnetic wave with electric field $$\vec{E}=E_{\max } \cos (k z-\omega t) \times \vec{j}$$ propagates in $$+z$$ direction. The origin is at the centre of the frame. (a) What is the magnetic flux through the coil in $$+x$$ direction. (b) What is the emf generated in the coil? (c) The electrommgntic wave has frequency $$4.4 \mathrm{MH} / \mathrm{z}$$, and intensity $$100 \mathrm{~W} / \mathrm{m}^{2}$$. The coil has $$N=50$$ windings and side length $$a=10 \mathrm{~cm}$$. Its self-inductance is $$L=74.0 \mu \mathrm{H}$$. The resistance $$R$$ of the circuit is 100 ohms. What value of copacitance $$C$$ results in resonant frequency for the $$R L C$$ circuit presented? (d) What $$I_{r m n}$$ flows in that case? A) no solution for $$(b)$$ is correct solution for (b) is $E=2 \times N \times E_{\max } \times \sin \left(\frac{k \times a}{2}\right) \times \sin (\omega \times t)$ solution for (c) is $$172 \mathrm{nf}$$. solution for $$(\mathrm{c})$$ is $$172 \mathrm{ppF}$$ solution for (d) is $$21.1 \mathrm{~mA}$$ solution for (b) is $\varepsilon=2 \times N \times a \times E_{\max } \times \sin \left(\frac{k \times e}{2}\right) \times \cos (\omega \times t)$ sovveion for $$(\mathrm{b})$$ is $\varepsilon=N \times a \times E_{\max } \times \sin \left(\frac{k \times a}{2}\right) \times \sin (\omega \times t)$ solution for $$(a)$$ is $\Phi_{B}=\frac{\alpha \times F_{m i}}{\omega} \times 2 \times \sin \left(\frac{k \times a}{2}\right) \times \cos (\omega \times t)$ solution for fol is 21, 1 A solution for fby is $\varepsilon=2 \times N \times a \times E_{\max } \times \sin \left(\frac{k \times a}{2}\right) \times \sin (\omega \times t)$ no solution for fat is correct. solution for (ldi is 19.1 A solution for (c) is 20 Bpf solution fue (s) is 21,1 solution for (a) is $\Phi_{B}=\frac{a \times F_{-i o}}{a} \times 2 \times \sin \left(\frac{k \times a}{2}\right) \times \cos (\alpha \times t)$ solution for ta) is $\Phi_{B}=\frac{a \times F_{m}}{\omega} \times 2 \times \cos \left(\frac{k \times a}{2}\right) \times \sin (\omega \times t)$ $\Phi_{B}=\frac{a \times E_{\max }}{\omega} \times 2 \times \cos \left(\frac{k \times a}{2}\right) \times \sin (\omega \times t)$ no solution for (c) is correct solution for (a) is $\Phi_{B}=\frac{a \times E_{\max }}{\omega} \times 2 \times \cos \left(\frac{k \times a}{4}\right) \times \sin (\omega \times t)$ no solution for (a) is correct solution for $$(c)$$ is $$20.3 \mathrm{nF}$$

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