Tutorial 4
SIF2003
1) Check whether the following fields are genuine EM fields, i.e., they satisfy
Maxwell's equations. Assume that the fields exist in charge-free regions
(a) 𝑨 = 40 𝑠𝑖𝑛 (𝜔𝑡 + 10𝑥)𝒂𝑧
(b) 𝑩 = 10 𝑐𝑜𝑠 (𝜔𝑡 − 2𝜌)𝒂𝜙 ⁄𝜌
(c) 𝑪 = (3𝜌2 𝑐𝑜𝑡 𝜙𝒂𝜌 + 𝑐𝑜𝑠 𝜙𝒂𝜙 ⁄𝜌) 𝑠𝑖𝑛 𝜔𝑡
(d) 𝑫 = 𝑠𝑖𝑛 𝜃 𝑠𝑖𝑛(𝜔𝑡 − 5𝑟)𝒂𝜙 ⁄𝑟
2) In free space,
𝑯 = 𝜌(𝑠𝑖𝑛 𝜙𝒂𝜌 + 2𝑐𝑜𝑠 𝜙𝒂𝜙 ) 𝑐𝑜𝑠 (4 × 106 𝑡) A/m
find Jd and E.
3) An antenna radiates in free space and
H
12 sin 
cos 2  10 8 t  βr a  mA / m
r


Find the corresponding E in terms of β
4) The electric field in air is given by E  ρte  ρ t aφ V/m. Find B and J.