Which of the following is a wrong statement?

  • A
    An emf can be induced between the ends of a straight conductor by moving it through a uniform magnetic field.
  • B
    The self-induced emf produced by changing current in a coil always tends to decrease the current.
  • C
    Inserting an iron core in a coil increases its coefficient of self-induction.
  • D
    According to Lenz's law,the direction of the induced current is such that it opposes the flux change that causes it.

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$A$ thin conducting rod $MN$ of mass $20 \text{ g}$,length $25 \text{ cm}$ and resistance $10 \text{ }\Omega$ is held on frictionless,long,perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field $B_0 = 4 \text{ T}$ directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time $t = 0$ and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-$I$ with an appropriate value from List-$II$,and choose the correct option. [Given: The acceleration due to gravity $g = 10 \text{ m s}^{-2}$ and $e^{-1} = 0.4$]
List-$I$List-$II$
$(P)$ At $t = 0.2 \text{ s}$,the magnitude of the induced emf in Volt$(1)$ $0.07$
$(Q)$ At $t = 0.2 \text{ s}$,the magnitude of the magnetic force in Newton$(2)$ $0.144$
$(R)$ At $t = 0.2 \text{ s}$,the power dissipated as heat in Watt$(3)$ $1.20$
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$(5)$ $2.00$

When a coil is placed in a time-dependent magnetic field,the power dissipated in it is $P$. The number of turns,area of the coil,and radius of the coil wire are $N, A$,and $r$ respectively. For a second coil,the number of turns,area,and radius are $2N, 2A$,and $3r$ respectively. When the first coil is replaced with the second coil,the power dissipated in it is $\alpha P$. The value of $\alpha$ is . . . . . . .

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