Time-harmonic magnetic field in a nonideal capacitor – 2-D movie. The electrodes of...

Time-harmonic magnetic field in a nonideal capacitor – 2-D movie. The electrodes of a parallel-plate capacitor are circular plates of radius a = 8 cm, as shown in Fig.6.9. The dielectric between the plates is imperfect, with parameters ε_r = 12, σ = 4× 10⁻⁴ S/m, and μ_r = 1, and the plate separation is d = 4 mm. The capacitor is connected

to a time-varying voltage v(t) = V₀ cos ωt, with V₀ = 1 V and ω = 10⁶ rad/s. As d _ a, the fringing effects can be neglected. Equations (3.5), (6.12), and (2.2) give (Fig.6.9) J(t) = σE(t) and Jd(t) = ε dE/dt, where E(t) = v(t)/d. Due to symmetry, the lines of the vector H in the dielectric are circles centered at the capacitor axis perpendicular to the plates, so that applying Eq.(6.11) to a circular contour C of radius r (r < a) in Fig.6.9, in exactly the same way as in Fig.4.10(b) and

Eqs.(4.15) and (4.16), yields

Create a 2-D movie in MATLAB that shows the distribution of the magnetic field intensity vector in the dielectric of the capacitor, during the course of time. (ME6 11.m on IR).

HINT: Use Eq.(6.13) and see MATLAB Exercises 4.15 (for the visualization of the 2-D spatial distribution of H by MATLAB function quiver) and 6.6 (for the representation of the temporal variation of H in a movie employing MATLAB function getframe).

Reference: Equations (3.5), (6.12), and (2.2), Eq(6.11), Eqs(4.15) and(4.16)

Reference: Figure 6.9, Fig.4.10(b)