Electromagnetic Waves

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Displacement current is a current due to a changing electric field in space or capacitor gap, given by $ i_d = \varepsilon_0 \frac{d\phi_E}{dt} $. It is necessary to maintain continuity of current in …

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The Ampere-Maxwell law is: $ \oint \vec{B} \cdot \vec{dl} = \mu_0 (i_c + i_d) = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt} $. It states that magnetic fields are produced by both conduction cur…

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Displacement current $ i_d $ equals the conduction current in the wire. Given: $ i_c = 1.5 \, \text{A} $. Therefore, $ i_d = 1.5 \, \text{A} $.

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According to Maxwell, a time-varying electric field generates a magnetic field, just as a current does. This is the displacement current effect. For example, during capacitor charging, the changing el…

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Use $ B_0 = \frac{E_0}{c} $. $ c = 3 \times 10^8 \, \text{m/s} $. Step 1: $ B_0 = \frac{120}{3 \times 10^8} = 4 \times 10^{-7} \, \text{T} $. Answer: $ 4 \times 10^{-7} \, \text{T} $.

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The speed is $ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \, \text{m/s} $. This is the speed of light, confirming that light is an EM wave.

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Use $ B = \frac{E}{c} $. $ c = 3 \times 10^8 \, \text{m/s} $. Step 1: $ B = \frac{8.1}{3 \times 10^8} = 2.7 \times 10^{-8} \, \text{T} $. Answer: $ 2.7 \times 10^{-8} \, \text{T} $.

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Electric field: $ E_x = E_0 \sin(kz - \omega t) $. Magnetic field: $ B_y = B_0 \sin(kz - \omega t) $. Both are perpendicular to each other and to the direction of propagation.