The field B at the centre of a circular coil of radius -r is $π$ times that due to a long straight wire at a distance r from it, for equal currents. Fig. shows three cases in
all cases the circular part has radius r and straight ones are infinitely long. For same current the field B at the centre P in cases 1, 2, 3 has the ratio

Question

The field B at the centre of a circular coil of radius -r is $π$ times that due to a long straight wire at a distance r from it, for equal currents. Fig. shows three cases in

all cases the circular part has radius r and straight ones are infinitely long. For same current the field B at the centre P in cases 1, 2, 3 has the ratio

Infinity Learn · Accepted Answer

In fig.(a) the magnetic fie]d induction at point P is given $$byB1=$$−$$B2$$−π$$B2+B2=$$−π$$B2$$…………………(1)In$$ fig. $$(b) the $$ma8netic$$ induction at point P is given $$byB2=$$π$$B2$$……………………………………………(2)In$$ fig. $$(c), the magnetic field induction at point P is given $$byB3=3$$$$π$$$$B4$$−$$B2=3$$$$π$$$$4$$−$$12B$$̣………………….(3)∴ $$B1$$:$$B2$$:$$B3=$$−π$$B2$$:π$$B2$$:$$3$$$$π$$$$4$$−$$12B=$$−π$$2$$:π$$2$$:$$3$$$$π$$$$4$$−$$12$$

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