Electronic Science and Technology Rabindra Kishore Mishra Lecture 8- Halfwave Dipole Introduction EST-E-335: Radiation System 3 Credits Electronic Science and Technology Rabindra Kishore Mishra Outline ➢Source and Observation Point ➢Current Source ➢Vector Potential ➢General Expression for Fields ➢Radiation Field ➢Problem set discussion Electronic Science and Technology Rabindra Kishore Mishra Source and Observation Point Electronic Science and Technology Rabindra Kishore Mishra Source and Observation Point Electronic Science and Technology Rabindra Kishore Mishra Source and Observation Point Electronic Science and Technology Rabindra Kishore Mishra Source and Observation Point Electronic Science and Technology Rabindra Kishore Mishra Current Source ➢𝐼 𝑧 = 𝐼𝑚 𝑠𝑖𝑛 𝑘 𝐼1 > 𝐼2 𝜆 4 − 𝑧 , 𝑧 ≤ 𝐼1 = 𝐼2 𝜆 4 Electronic Science and Technology Rabindra Kishore Mishra Vector Potential 𝜇 𝒋 𝒓′ 𝑒 −𝑗𝒌.𝑹 3 ′ 1 ➢𝑨 𝒓 = 𝑑𝒓 4𝜋 𝑅 −𝑗𝑘 𝑘.(𝒓−𝒓′) 𝜇 ′ ′ ′ 𝑒 = 𝑧Ƹ 𝑧 𝐼 𝑦 𝛿 𝑥 𝛿 𝑑𝑥′𝑑𝑦′𝑑𝑧′ 4𝜋 (𝒓−𝒓′) −𝑗𝑘𝑘.(𝒓−𝒓′) 𝜇 𝑒 ′ = 𝑧Ƹ 𝑧 𝐼 𝑑𝑧′ 4𝜋 (𝒓−𝒓′) 𝜇𝑒 −𝑗𝑘𝑟 ➢𝑨 = 𝑧Ƹ 𝐼 𝑧 ′ 𝑒 −𝑗𝑘𝑧′ cos 𝜃 4𝜋𝑟 𝑑𝑧′ Electronic Science and Technology Rabindra Kishore Mishra General Expression for Fields ➢𝑬 = −𝑗𝜔𝑨 ➢𝑬 = −𝑗𝜔𝑨 − −𝑗𝜔𝑨. 𝑟Ƹ 𝑟Ƹ = −𝑗𝜔(𝐴𝜃 𝜃መ + 𝐴𝜑 𝜑) ො ➢𝑬 = −𝑗𝜔 sin 𝜃 𝐴𝑧 𝜃መ 1 ➢𝑯 = 𝑟Ƹ × 𝜂 𝐸𝜃 ➢𝐻𝜑 = 𝜂 𝑬 Electronic Science and Technology Rabindra Kishore Mishra Radiation Field 2𝐼𝑚 𝑒 −𝑗𝑘𝑟 cos[(𝜋/2) 𝑐𝑜𝑠𝜃] ➢𝐸𝜃 = 𝑗𝜔𝜇 sin 𝜃 𝑘 4𝜋𝑟 𝑠𝑖𝑛2 𝜃 cos[(𝜋/2) 𝑐𝑜𝑠𝜃] ➢𝑓 𝜃 = , 𝑔 𝜃 = 𝑠𝑖𝑛𝜃 2 𝑠𝑖𝑛 𝜃 cos[(𝜋/2) 𝑐𝑜𝑠𝜃] ➢𝐹 𝜃 = 𝑔 𝜃 𝑓 𝜃 = 𝑠𝑖𝑛𝜃 Electronic Science and Technology Rabindra Kishore Mishra Field Animation Electronic Science and Technology Rabindra Kishore Mishra Radiation Field Electronic Science and Technology Rabindra Kishore Mishra Problem set 1 Electronic Science and Technology Rabindra Kishore Mishra Problem set 1 Electronic Science and Technology Rabindra Kishore Mishra Problem set 1 Electronic Science and Technology Rabindra Kishore Mishra Problem set 1 Electronic Science and Technology Rabindra Kishore Mishra Problem set 1 Electronic Science and Technology Rabindra Kishore Mishra
