A long solenoid of radius R carries a time (t) - dependent current I(t) = I0t(1 — t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 le t le 1, the induced current (IR) and the induced EMF(VR) in the ring change as :

Question

A long solenoid of radius R carries a time (t) - dependent current I(t) = I0t(1 — t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 le t le 1, the induced current (IR) and the induced EMF(VR) in the ring change as : (A) Direction of IR remains unchanged and VR is zero at t =0.25 (B) Direction of IR remains unchanged and VR is maximum at t = 0.5 (C) At t =0.25 direction of IR reverses and VR is maximum (D) At t = 0.5 direction of IR reverses and VR is zero

Tardigrade Admin · Accepted Answer

I=I0t-I0t2 φ=BA φ=μ0nIA VR=-(dφ/dt)=-μ0nAI0(1-2t) VR=0 at t=(1/2) and IR=(VR/Resistance of loop)

Q. A long solenoid of radius R carries a time (t) - dependent current $I (t) = I_{0} t (1— t)$ . A ring of radius $2 R$ is placed coaxially near its middle. During the time interval $0 \leq t \leq 1,$ the induced current $(I_{R})$ and the induced $EMF (V_{R})$ in the ring change as :

Direction of $I_{R}$ remains unchanged and $V_{R}$ is zero at $t = 0.25$

Direction of $I_{R}$ remains unchanged and $V_{R}$ is maximum at $t = 0.5$

At $t = 0.25$ direction of $I_{R}$ reverses and $V_{R}$ is maximum

At $t = 0.5$ direction of $I_{R}$ reverses and $V_{R}$ is zero

$I = I_{0} t - I_{0} t^{2}$
$ϕ = B A$
$ϕ = μ_{0} n I A$
$V_{R} = - \frac{d ϕ}{d t} = - μ_{0} n A I_{0} (1 - 2 t)$
$V_{R} = 0 a tt = \frac{1}{2}$
and $I_{R} = \frac{V _{R}}{R es i s t an ce o f l oo p}$

Q. A long solenoid of radius R carries a time (t) - dependent current I(t)=I0​t(1—t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0≤t≤1, the induced current (IR​) and the induced EMF(VR​) in the ring change as :

Direction of IR​ remains unchanged and VR​ is zero at t=0.25

Direction of IR​ remains unchanged and VR​ is maximum at t=0.5

At t=0.25 direction of IR​ reverses and VR​ is maximum

At t=0.5 direction of IR​ reverses and VR​ is zero