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Match the following

Column-I

Column-II
(A)
A conducting loop is placed on horizontal xy plane in a uniform vertical magnetic field $\vec{B} = \frac{B_{0}}{t^{2}} T^{2} (\hat{k})$ where T is a constant. The radius of the loop is increasing continuously as $r = \frac{(r_{0} t)}{Δ T},$ where t is starting from a value t→0

(p)
An induced current
(B)
A fixed long conducting cylinder of length l , radius R and thickness t (where l≫R and where l≫t) having an initial current I_0..
(q)
An electrostatic field
(C)
A non conducting solid cylinder of length l, radius R(R≪l) having uniform volume charge density ρ is rotating about its central axis with constant angular velocity ω by some external agent.
(r)
An induced electric field
(D)
An infinite sheet of surface charge density σ placed on xy plane and moving with velocity $\vec{v} = v_{0} \hat{l}$ and a conducting loop is fixed just above the sheet.
(s)
A steady magnetic field
The correct option is:

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(I)-(S) (II)-(R) (III)-(Q) (IV)-(Q, S)

(I)-(R) (II)-(S) (III)-(Q) (IV)-(P)

(I)-(R) (II)-(S) (III)-(Q, S) (IV)-(Q, S)

(I)-(S) (II)-(Q) (III)-(S) (IV)-(Q)

answer is C.

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Detailed Solution

(I) $ϕ_{l o o p} =$ constant wrt time.
emf = 0, electrostatic field = 0, but B = f(t)
$\Rightarrow$ included electric field is present
Ans. I – R
(II) It is like long solenoid
Hence steady magnetic field
Ans. II – S
(III) Isolated charge $\to$ electrostatic field
Rotating charge $\to$ average current  steady magnetic field
Ans. III – QS
(IV) Isolated charge $\to$ electrostatic field
Rotating charge $\to$ average current $\to$ steady magnetic field
Ans. III – QS

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