A long solenoid of diameter 0.1 m has 2 × 104 turns per

A long solenoid of diameter 0.1 m has 2 × 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 0A from 4 A in 0.05 s. If the resistance of the coil is 10π²Ω. the total charge flowing through the coil during this time is :-

Given, no. of turns N = 100 radius,
r = 0.01 m
resistance, R = 10π2Ω, n = 2 × 10⁴
As we know,

ε = -N	dφ
	dt

	ε	= -	N		dφ
	R		R		dt

ΔI = -	N		dφ
	R		dt

	Δq	= -	N		Δφ
	Δt		R		Δt

Δ q = -		N			Δφ			Δt
		R			Δt

'–' ve sign shows that induced emf opposes the change of flux.

Δ q = -		μ₀nNπr²		Δi			1	Δt
				Δt			R

=	μ₀nNπr²Δi
	R

Δq =	4π × 10^-7 × 100 × 4 × π (0.01)² × 2 × 10⁴
	10π²

Δq = 32μC