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www.GOALias.blogspot.coma consequence of the displacement current being a source of a magneticfield. Thus, time- dependent electric and magnetic fields give rise to eachother! Faraday’s law of electromagnetic induction and Ampere-Maxwelllaw give a quantitative expression of this statement, with the currentbeing the total current, as in Eq. (8.5). One very important consequenceof this symmetry is the existence of electromagnetic waves, which wediscuss qualitatively in the next section.MAXWELL’S EQUATIONSElectromagneticWaves1. ∫ Eid A = Q / ε02. ∫ Bid A =03.–dΦB∫ Eid= l dtdΦE ∫ B d= μ μ εdt4. i l 0i c+0 0(Gauss’s Law for electricity)(Gauss’s Law for magnetism)(Faraday’s Law)(Ampere – Maxwell Law)Example 8.1 A parallel plate capacitor with circular plates of radius1 m has a capacitance of 1 nF. At t = 0, it is connected for charging inseries with a resistor R = 1 M Ω across a 2V battery (Fig. 8.3). Calculatethe magnetic field at a point P, halfway between the centre and theperiphery of the plates, after t = 10 –3 s. (The charge on the capacitorat time t is q (t) = CV [1 – exp (–t/τ )], where the time constant τ isequal to CR.)FIGURE 8.3Solution The time constant of the CR circuit is τ = CR = 10 –3 s. Then,we haveq(t) = CV [1 – exp (–t/τ)]= 2 × 10 –9 [1– exp (–t/10 –3 )]The electric field in between the plates at time t is( )qt qE = ε0A= ε; A = π π (1) 2 m 2 = area of the plates.0Consider now a circular loop of radius (1/2) m parallel to the platespassing through P. The magnetic field B at all points on the loop isEXAMPLE 8.1273