Problem 4: Two electric blankets heating systems are proposed as shown in Figure

Question

Problem 4: Two electric blankets heating systems are proposed as shown in Figure A and B (viewed from above). Suppose that in either case, the current in each wire is equal to 1=1 A, there are N=100 wires and the length d=2 m. Calculate the magnetic fiel intensity above the blanket in cach case. Which system produces a lower magnetic field intensity and why? Note: This solution was proposed for electric blankets when health concerns due magnetic fields arose. H=N wires Figure B Figure A TLAB Tall; cle; N=100; d=2; %find Ha for Figure A %find Hb for Figure B ver: e A magnetic field HA = B magnetic field HB =

Explanation / Answer

In figure 1, current divided into N lines. Thus current flowing through each line is I/N=1/100=0.01A

Since current flows in same direction in all wires, net H is due to first and last wire only as H due to wires in between gets cancelled. So, H=(100)(0.01+0.01)/(2)=1 A/m

In second case, current changes its direction on every turn, therefore net field gets added up. So, H=100*1/2=50 A/m

%Any doubts, plz ask. Thumbs down won't solve your doubt. Thanks!

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