First slide

Magnetic Flux

Question

A long solenoid of diameter 0.1 m has 2 x 10⁴ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.0 I m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to OA from 4A in 0.05 s. If the resistance of the coil is 10 $π^{2} Ω$ . The total charge flowing through the coil during this time is :

Moderate

A

16 μC
B

32μC
C

16 $π$ μC
D

32 $π$ μC

Solution

$q = [(\frac{∆ ϕ}{∆ t}) . \frac{1}{R}] ∆ t q = [μ_{0} {nNπr}^{2} \frac{∆ i}{∆ t}] \frac{1}{R} ∆ t q = [4 π x 10^{- 7} x 2 x 10^{4} x 100 x π x {(10^{- 2})}^{2} x (\frac{4}{0.05})] \frac{1}{10 π^{2}} x 0.05 q = 32 μC$

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