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Question 5.9: Find the magnetic field at point P for each of the steady cu...

Find the magnetic field at point P for each of the steady current configurations shown in Fig. 5.23. 

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(a) The straight segments produce no field at P . The two quarter-circles give  B=\frac{\mu_{0} I}{8}\left(\frac{1}{a}-\frac{1}{b}\right) (out).

(b) The two half-lines are the same as one infinite line:  \frac{\mu_{0} I}{2 \pi R} ; the half-circle contributes  \frac{\mu_{0} I}{4 R} .

So B=\frac{\mu_{0} I}{4 R}\left(1+\frac{2}{\pi}\right) (into the page).

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