**Displacement current and Maxwell’s equations; Wave equations in vacuum,**

Questions:

**Q 1. **For the electric field given by $E= E_oe^{i\omega t}$, show that the conduction current is in phase with the electric field, while the displacement currents lead the electric field by $\pi/2$ radians. Also, show that the displacement current in a good conductor is negligible compared tp the conduction current at any frequency lower than the optical frequencies $(f<10^{15}Hz)$. ** ** ** [10 marks]**

**Q 2. ** Write Maxwell’s equations in free space in both differential and integral forms. Obtain wave equations and show that electromagnetic waves can travel in free space with the speed of light. **[10 marks]**

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