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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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