Question 96: Electromagnetic Induction

Question

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 $$ \le $$ t $$ \le $$ 1, the induced current (I
R
) and the induced EMF(V
R
) in the ring change as :

Accepted Answer

I(t) = I
0
t(1 - t)
We know, $$\phi $$ = BA
$$ \Rightarrow $$ $$\phi $$ = $$\mu $$
0
nIA
$$ \Rightarrow $$ $$\phi $$ = $$\mu $$
0
nAI
0
(t - t
2
)
Also V
R
= $$ - {{d\phi } \over {dt}}$$
= - $$\mu $$
0
nAI
0
(1 - 2t)
V
R
= 0 when 1 - 2t = 0
$$ \Rightarrow $$ t = 0.5
Also we know, V
R
= I
R
r
$$ \Rightarrow $$ I
R
= $${{{\mu _0}nA{I_0}\left( {1 - 2t} \right)} \over r}$$
after t = 0.5, I
R
reverses its direction.

Answer

Direction of I
R
remains unchanged and V
R
is zero at t = 0.25

Answer

Direction of I
R
remains unchanged and V
R
is maximum at t = 0.5

Answer

At t = 0.25 direction of I
R
reverses and V
R
is maximum

Answer

At t = 0.5 direction of I
R
reverses and V
R
is zero

Electromagnetic Induction

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 $ \le t \le $ 1, the induced current (I R ) and the induced EMF(V R ) in the ring change as :

Choose the correct answer: