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Electromagnetic Induction question

2017 · Q131
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Electromagnetic Induction question

2017 · Q131

NEETPhysicsElectromagnetic InductionMCQ+4 / −1
A long solenoid of diameter 0.1 m has 2 ×\times× 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 π\piπ2 Ω\OmegaΩ, the total charge flowing through the coil during this time is
  1. A
    16 μ\muμC
  2. B
    32 μ\muμC
  3. C
    16π\piπ μ\muμC
  4. D
    32π\piπ μ\muμC
View written solutionFree

Correct answer: B

q = −dϕR - {{d\phi } \over R}−Rdϕ​

= −NA(B2−B1)R - {{NA\left( {{B_2} - {B_1}} \right)} \over R}−RNA(B2​−B1​)​

= NAμ0n(i1−i2)R{{NA{\mu _0}n\left( {{i_1} - {i_2}} \right)} \over R}RNAμ0​n(i1​−i2​)​

= 100×π×10−4×4π×10−7×2×104×410π2{{100 \times \pi \times {{10}^{ - 4}} \times 4\pi \times {{10}^{ - 7}} \times 2 \times {{10}^4} \times 4} \over {10{\pi ^2}}}10π2100×π×10−4×4π×10−7×2×104×4​

= 32 ×\times× 10-6 C = 32 μ\mu μC

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