A long solenoid of radius R carries a time (t) $$-$$ dependent current $$It=I0t1$$−t. A ring of radius $$2R$$ is placed coaxially near its middle. During the time interval $$0$$≤t≤$$1$$, the inducted current IR and the induced EMF (VR) in the ring changes as:

Question

A long solenoid of radius R carries a time (t) $$-$$ dependent current  $$It=I0t1$$−t. A ring of radius $$2R$$ is placed coaxially near its middle. During the time interval  $$0$$≤t≤$$1$$, the inducted current IR  and the induced EMF (VR) in the ring changes as:

Infinity Learn · Accepted Answer

Current, $$I=I0t$$−$$I0t2$$           ​Magnetic flux,  ϕ$$=BA=$$μ$$0nIA$$​Induced emf, $$VR=$$−dϕ$$dt=$$−μ$$0nAI01$$−$$2t$$ Hence, $$VR=0$$ at $$t=12$$     And ​$$IR=VRResistance$$ of loopSo, $$0$$

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

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A long solenoid of radius R carries a time (t) - dependent current It=I0t1−t. A ring of radius 2R is placed coaxially near its middle. During the time interval 0≤t≤1, the inducted current IR and the induced EMF (VR) in the ring changes as:

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