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Q.

A triangular loop ABCA of resistance ‘R’ is placed at a distance ‘a’ from a long straight current carrying wire having current I. Choose the correct options.

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a

Mutual inductance of the system in the given position is μ0a2π[1−ℓn2].

b

Mutual inductance of the system in the given position is μ0a2π[1+ℓn2]

c

If the coil is rotated by 180o about side AB, the charge flow in the loop is μ0ia2πRℓn2716

d

If the coil is rotated by 180o about side AB, the charge flow in the loop is μ0iaπRℓn43

answer is A.

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Detailed Solution

ϕi=∫0aμ0i2π(a+x)xdx=μ0ia2π[1−ℓn2]M=ϕii=μ0a2π[1−ℓn2]ϕf=∫0aμ0i(a-x)dxcos(1800)2π(x+2a)=μ0ia2π[1−3ℓn32]Induced emf=ϕf-ϕi△t⇒△q△tR=ϕf-ϕi△t ⇒△q=μ0ia2πR[ℓn2716]
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