Question

Two cars are approaching one another. Car A moves to the right at speed c/4 and car B moves to the left at speed e/6. Where c is the speed of sound. Car B transmits a signal of frequency 1000 Hz. The receiver on car. A will detect a frequency (in H_z) of 1500 1071 900 643 The components of a magnetic field in a region of space is given by: (B_x, B_y, B_z) = (St, D, Ft) where S, D and F are constants and t is time. There is a circular loop of area A in the x - y plane. Find the E.M.F. induced around the loop. -SA -F SFDA, -FA Two concentric loops of wire of radii a and b carry currents I and I' in opposite. Let a = 0.1 m, b = 0.2 m, I = 20 A and I' = 5A. Find the magnetic field at the center 9.42 times 10^-5 T 1.00 times 10^-5 3.14 times 10^-5 T, 3.00 times 10^-5 T

Answer 1

4) Applying Doppler shift formula we get

$f'=\frac{c+v_o}{c-v_s}\times f \quad \quad \text{c=speed of sound,} v_o=\text{speed of observer},v_s=\text{speed of source} \\ \implies f'=\frac{c+\frac{c}{4}}{c-\frac{c}{6}}\times1000\\ \implies f'=1500Hz$

5)Flux is $\Phi=\vec{B}\cdot\vec{A}=Ft$

Induced EMF is $\varepsilon=-\frac{d\Phi}{dt}=-F$

6)Magnetic field is

$\frac{\mu_0}{2}\left( \frac{I}{a}-\frac{I'}{b}\right )\\ =\frac{\mu_0}{2}\left( \frac{20}{0.1}-\frac{5}{0.2}\right )\\ =1.099\times10^{-4}T$