ᴀ ᴋɴᴜᴄᴋʟᴇ ᴊᴏɪɴᴛ ɪꜱ ᴛᴏ ʙᴇ ᴀxɪᴀʟʟʏ ʟᴏᴀᴅᴇᴅ ᴡɪᴛʜ ᴀ ᴛᴇɴꜱɪʟᴇ ʟᴏᴀᴅ ꜰ. ᴛʜᴇ ᴀꜱꜱᴇᴍʙʟʏ ᴏꜰ ᴘᴀʀᴛꜱ ᴀɴᴅ ᴛʜᴇɪʀ ᴠᴀʀɪᴀʙʟᴇ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴀʀᴇ ꜱʜᴏᴡɴ ɪɴ ᴛʜᴇ ꜰɪɢᴜʀᴇ ʙᴇʟᴏᴡ. ᴡʀɪᴛᴇ ᴛʜᴇ ꜱᴛʀᴇꜱꜱ ᴇQᴜᴀᴛɪᴏɴ ᴀᴛ ᴇᴀᴄʜ ᴏꜰ ᴛʜᴇ ᴘᴏꜱꜱɪʙʟᴇ ʟᴏᴄᴀᴛɪᴏɴꜱ ᴏꜰ ꜰᴀɪʟᴜʀᴇ. ɪᴅᴇɴᴛɪꜰʏ ᴇᴀᴄʜ ꜱᴛʀᴇꜱꜱ ᴀɴᴅ ᴡʀɪᴛᴇ ɪᴛꜱ ᴇQᴜᴀᴛɪᴏɴ ɪɴ ᴛᴇʀᴍꜱ ᴏꜰ ᴛʜᴇ ʟᴏᴀᴅ ꜰ, ᴀɴᴅ ᴛʜᴇ ɢɪᴠᴇɴ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴀ, ʙ, ᴄ, ᴅ, ᴋ, ᴍ ᴀɴᴅ ɴ. (ᴇxᴀᴍᴘʟᴇ: ᴛᴇɴꜱɪʟᴇ ꜱᴛʀᴇꜱꜱ ᴀᴛ ᴛʜᴇ ʀᴏᴅ ᴏꜰ ᴛʜᴇ ᴋɴᴜᴄᴋʟᴇ ᴊᴏɪɴᴛ: ꜱᴛ = 4ꜰ/Πᴅ2). ᴅᴏɴ’ᴛ ᴜꜱᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴛʜᴀᴛ ᴀʀᴇ ɴᴏᴛ ᴅᴇꜰɪɴᴇᴅ ɪɴ ᴛʜᴇ ᴊᴏɪɴᴛ ᴅᴇꜱᴄʀɪʙᴇᴅ ʙᴇʟᴏᴡ. ꜱᴜᴘᴘᴏʀᴛ ᴇᴀᴄʜ ᴏꜰ ᴛʜᴇ ꜱᴛʀᴇꜱꜱ ᴇQᴜᴀᴛɪᴏɴꜱ ʙʏ ᴍᴇᴀɴꜱ ᴏꜰ ᴀɴ ɪꜱᴏᴍᴇᴛʀɪᴄ ᴅʀᴀᴡɪɴɢ ɪɴᴅɪᴄᴀᴛɪɴɢ ᴛʜᴇ ᴘᴀʀᴛ ᴀɴᴅ ɪᴛꜱ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴛʜᴀᴛ ᴍɪɢʜᴛ ʜᴀᴠᴇ ꜰᴀɪʟᴇᴅ ᴅᴜᴇ ᴛᴏ ᴏᴠᴇʀꜱᴛʀᴇꜱꜱɪɴɢ. ꜰᴏʀ ᴛʜᴇ ʙᴇɴᴅɪɴɢ ꜱᴛʀᴇꜱꜱ ɪɴ ᴛʜᴇ ᴘɪɴ, ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ʟᴏᴀᴅꜱ ᴛᴏ ʙᴇ ᴜɴɪꜰᴏʀᴍʟʏ ᴅɪꜱᴛʀɪʙᴜᴛᴇᴅ ᴀᴛ ᴛʜᴇ ᴄᴇɴᴛᴇʀ ᴏꜰ ᴛʜᴇ ᴄᴏᴛᴛᴇʀ ᴀɴᴅ ᴜɴɪꜰᴏʀᴍʟʏ ᴠᴀʀʏɪɴɢ ᴀᴛ ᴛʜᴇ ᴋɴᴜᴄᴋʟᴇ ᴇɴᴅ. ɴᴇɢʟᴇᴄᴛ ᴛʜᴇ ᴘʀᴇꜱᴇɴᴛ ᴏꜰ ᴛʜᴇ ꜰɪʟʟᴇᴛꜱ ɪɴ ᴄᴏɴꜱɪᴅᴇʀɪɴɢ ᴛʜᴇ ᴅɪᴍᴇɴꜱɪᴏɴꜱ

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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ᴘᴀʀᴛ ᴀ.
ᴀ ᴋɴᴜᴄᴋʟᴇ ᴊᴏɪɴᴛ ɪꜱ ᴛᴏ ʙᴇ ᴀxɪᴀʟʟʏ ʟᴏᴀᴅᴇᴅ ᴡɪᴛʜ ᴀ ᴛᴇɴꜱɪʟᴇ ʟᴏᴀᴅ ꜰ. ᴛʜᴇ ᴀꜱꜱᴇᴍʙʟʏ ᴏꜰ ᴘᴀʀᴛꜱ ᴀɴᴅ ᴛʜᴇɪʀ ᴠᴀʀɪᴀʙʟᴇ
ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴀʀᴇ ꜱʜᴏᴡɴ ɪɴ ᴛʜᴇ ꜰɪɢᴜʀᴇ ʙᴇʟᴏᴡ. ᴡʀɪᴛᴇ ᴛʜᴇ ꜱᴛʀᴇꜱꜱ ᴇQᴜᴀᴛɪᴏɴ ᴀᴛ ᴇᴀᴄʜ ᴏꜰ ᴛʜᴇ ᴘᴏꜱꜱɪʙʟᴇ ʟᴏᴄᴀᴛɪᴏɴꜱ ᴏꜰ ꜰᴀɪʟᴜʀᴇ. ɪᴅᴇɴᴛɪꜰʏ ᴇᴀᴄʜ ꜱᴛʀᴇꜱꜱ ᴀɴᴅ ᴡʀɪᴛᴇ ɪᴛꜱ ᴇQᴜᴀᴛɪᴏɴ ɪɴ ᴛᴇʀᴍꜱ ᴏꜰ ᴛʜᴇ ʟᴏᴀᴅ ꜰ, ᴀɴᴅ ᴛʜᴇ ɢɪᴠᴇɴ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴀ, ʙ, ᴄ, ᴅ, ᴋ, ᴍ ᴀɴᴅ ɴ. (ᴇxᴀᴍᴘʟᴇ: ᴛᴇɴꜱɪʟᴇ ꜱᴛʀᴇꜱꜱ ᴀᴛ ᴛʜᴇ ʀᴏᴅ ᴏꜰ ᴛʜᴇ ᴋɴᴜᴄᴋʟᴇ ᴊᴏɪɴᴛ: ꜱᴛ = 4ꜰ/Πᴅ2). ᴅᴏɴ’ᴛ ᴜꜱᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴛʜᴀᴛ ᴀʀᴇ ɴᴏᴛ ᴅᴇꜰɪɴᴇᴅ ɪɴ ᴛʜᴇ ᴊᴏɪɴᴛ ᴅᴇꜱᴄʀɪʙᴇᴅ ʙᴇʟᴏᴡ. ꜱᴜᴘᴘᴏʀᴛ ᴇᴀᴄʜ ᴏꜰ ᴛʜᴇ ꜱᴛʀᴇꜱꜱ ᴇQᴜᴀᴛɪᴏɴꜱ ʙʏ ᴍᴇᴀɴꜱ ᴏꜰ ᴀɴ ɪꜱᴏᴍᴇᴛʀɪᴄ ᴅʀᴀᴡɪɴɢ ɪɴᴅɪᴄᴀᴛɪɴɢ ᴛʜᴇ ᴘᴀʀᴛ ᴀɴᴅ ɪᴛꜱ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴛʜᴀᴛ ᴍɪɢʜᴛ ʜᴀᴠᴇ ꜰᴀɪʟᴇᴅ ᴅᴜᴇ ᴛᴏ ᴏᴠᴇʀꜱᴛʀᴇꜱꜱɪɴɢ. ꜰᴏʀ ᴛʜᴇ ʙᴇɴᴅɪɴɢ ꜱᴛʀᴇꜱꜱ ɪɴ ᴛʜᴇ ᴘɪɴ, ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ʟᴏᴀᴅꜱ ᴛᴏ ʙᴇ ᴜɴɪꜰᴏʀᴍʟʏ ᴅɪꜱᴛʀɪʙᴜᴛᴇᴅ ᴀᴛ ᴛʜᴇ ᴄᴇɴᴛᴇʀ ᴏꜰ ᴛʜᴇ ᴄᴏᴛᴛᴇʀ ᴀɴᴅ ᴜɴɪꜰᴏʀᴍʟʏ ᴠᴀʀʏɪɴɢ ᴀᴛ ᴛʜᴇ ᴋɴᴜᴄᴋʟᴇ ᴇɴᴅ. ɴᴇɢʟᴇᴄᴛ ᴛʜᴇ ᴘʀᴇꜱᴇɴᴛ ᴏꜰ ᴛʜᴇ ꜰɪʟʟᴇᴛꜱ ɪɴ ᴄᴏɴꜱɪᴅᴇʀɪɴɢ ᴛʜᴇ ᴅɪᴍᴇɴꜱɪᴏɴꜱ
ᴘᴀʀᴛ ʙ.
ᴜꜱɪɴɢ ᴛʜᴇ ꜱᴛʀᴇꜱꜱ ᴇQᴜᴀᴛɪᴏɴꜱ ꜰᴏʀᴍᴇᴅ ɪɴ ᴘᴀʀᴛ ᴀ, ᴅᴇꜱɪɢɴ ᴛʜᴇ ᴊᴏɪɴᴛ ʙʏ ꜱᴘᴇᴄɪꜰʏɪɴɢ ᴛʜᴇ ʀᴇQᴜɪʀᴇᴅ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴛꜱ. ᴛʜᴇ ᴊᴏɪɴᴛ ɪꜱ ᴛᴏ ʜᴀɴᴅʟᴇ ᴀ ᴍᴀxɪᴍᴜᴍ ᴛᴇɴꜱɪʟᴇ ʟᴏᴀᴅ ᴏꜰ ꜰ = 20 ᴋɪᴘꜱ. ᴛʜᴇ ꜱᴏᴄᴋᴇᴛ ᴏʀ ʏᴏᴋᴇ ᴀɴᴅ ʀᴏᴅ ᴀʀᴇ ᴍᴀᴅᴇ ᴏꜰ ᴀɪꜱɪ ᴄ 1040, ɴᴏʀᴍᴀʟɪᴢᴇᴅ ꜱᴛᴇᴇʟ. ᴛʜᴇ ᴘɪɴ ɪꜱ ᴍᴀᴅᴇ ᴏꜰ ᴀɴ ᴀꜱ ʀᴏʟʟᴇᴅ ᴀɪꜱɪ ᴄ 1015 ꜱᴛᴇᴇʟ. ᴀꜱꜱᴜᴍᴇ ᴀ ꜰᴀᴄᴛᴏʀ ᴏꜰ ꜱᴀꜰᴇᴛʏ ᴏꜰ 3 ꜰᴏʀ ᴛʜᴇ ᴘɪɴ ᴀɴᴅ 4 ꜰᴏʀ ᴛʜᴇ ᴏᴛʜᴇʀ ᴘᴀʀᴛꜱ, ʙᴀꜱᴇᴅ ᴏɴ ᴛʜᴇ ʏɪᴇʟᴅ ᴘᴏɪɴᴛ. ᴜꜱᴇ ꜱʏꜱ = 0.5 ꜱʏ. ɪɴ ᴅɪᴍᴇɴꜱɪᴏɴɪɴɢ ᴏᴛʜᴇʀ ᴘᴀʀᴛꜱ, ᴛʜᴇ ꜰᴏʟʟᴏᴡɪɴɢ ᴘʀᴏᴘᴏʀᴛɪᴏɴꜱ ᴍᴀʏ ʙᴇ ᴀꜱꜱᴜᴍᴇᴅ: ᴀ= 0.75d; ʙ =0.25d; ᴄ=1.5d; ᴍ = 2.0d; ɴ = 2.0d; ᴋ = 2.25d ᴀꜱ ᴀɴ ᴏᴜᴛᴘᴜᴛ ᴏꜰ ᴘᴀʀᴛ ʙ, ᴘʀᴇꜱᴇɴᴛ ᴀ ꜱᴄᴀʟᴇᴅ ɪꜱᴏᴍᴇᴛʀɪᴄ ᴅʀᴀᴡɪɴɢ ᴏꜰ ᴛʜᴇ ᴊᴏɪɴᴛ ꜱʜᴏᴡɪɴɢ ᴀʟʟ ᴛʜᴇ ɪᴍᴘᴏʀᴛᴀɴᴛ ᴅɪᴍᴇɴꜱɪᴏɴꜱ ᴘʀᴇꜰᴇʀᴀʙʟʏ ɪɴ ᴛʜᴇɪʀ ᴘʀᴇꜰᴇʀʀᴇᴅ ꜱɪᴢᴇꜱ. ᴀꜱꜱᴜᴍᴇ ᴏᴛʜᴇʀ ᴘʀᴏᴘᴏʀᴛɪᴏɴꜱ ɪꜰ ɴᴇᴄᴇꜱꜱᴀʀʏ.

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