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Q.

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 inall 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

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a

−π2:π2:3π4−12

b

−π2+1:π2+1:3π4+12

c

−π2:π2:3π4

d

−π2−1:π4+14:3π4+12

answer is A.

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Detailed Solution

In fig.(a) the magnetic fie]d induction at point P is given byB1=−B2−πB2+B2=−πB2…………………(1)In fig. (b) the ma8netic induction at point P is given byB2=πB2……………………………………………(2)In fig. (c), the magnetic field induction at point P is given byB3=3πB4−B2=3π4−12Ḅ………………….(3)∴ B1:B2:B3=−πB2:πB2:3π4−12B=−π2:π2:3π4−12
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