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# Exercises **Exercise 2** In a Cartesian coordinate system R(O, ex, ey, ez), a surface charge density σ(t) = σ₀δ(ωt) is distributed on the plane P(x = 0). The electric field E(r,t) generated by this distribution, where r is the position vector and t is the time variable, is to be determined usin...

# Exercises **Exercise 2** In a Cartesian coordinate system R(O, ex, ey, ez), a surface charge density σ(t) = σ₀δ(ωt) is distributed on the plane P(x = 0). The electric field E(r,t) generated by this distribution, where r is the position vector and t is the time variable, is to be determined using the quasi-stationary approximation (ARQS). 1. **Justification of electric field form:** E(r,t) = E(x,t) * ex for any (r,t). 2. **Justification of property and calculation of E(r,t) on P(x = 0):** - E(-x,t) = -E(x,t) for all (x,t) - Determine E(r,t) on the plane P(x = 0). 3. **Expression for E(x,t) for x > 0 and x < 0:** - Express E(x,t) for x > 0. - Express E(x,t) for x < 0. 4. **Expression for scalar potential V(r,t):** - Express the scalar potential V(r,t) such that V(x = 0, t) = 0 (for all t). **Exercise 3** In a Cartesian coordinate system R(O, ex, ey, ez), a cylindrical rod with infinite height and radius R, with current density j(t) = j₀ cos(ωt) ez, is described. This current produces a magnetic field B at points outside the rod, which has a potential ϕ.