The circular plates of a parallel-plate capacitor have a radius of 30 mm. A steady 0.43-mA current is charging the initially uncharged capacitor, and the surface charge on the plates is distributed uniformly. The flat circular surface between the capacitor plates is coaxial and parallel to the plates, and has a radius of 13 mm. Calculate the magnetic field at any point on the circumference of the circular region (in Tesla).

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Agas is contained in a vertical, frictionless piston–cylinder device. the piston has a mass of 3.2 kg and a cross-sectional area of 35 cm2. a compressed spring above the piston exerts a force of 190 n on the piston. if the atmospheric pressure is 95 kpa, determine the pressure inside the cylinder.

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.