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(D) Given the magnetic field $B = 0.01 - 2t \, Tesla$.The rate of change of the magnetic field is $\frac{dB}{dt} = -2 \, Tesla/s$.The area of the loop

Vedclass · Accepted Answer

$9$

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(D) Given the magnetic field $B = 0.01 - 2t \, Tesla$.The rate of change of the magnetic field is $\frac{dB}{dt} = -2 \, Tesla/s$.The area of the loop inside the magnetic field is $A_{eff} = \frac{1}{2} 	imes (1 \, m)^2 = 0.5 \, m^2$.The induced $emf$ $(e)$ is given by Faraday's law of induction: $e = -\frac{d\phi}{dt} = -\frac{d}{dt}(B \cdot A_{eff})$.$e = -A_{eff} \cdot \frac{dB}{dt} = -(0.5 \, m^2) 	imes (-2 \, Tesla/s) = 1 \, V$.Since the magnetic field is decreasing,the induced $emf$ acts in a direction that opposes the change. According to Lenz's law,the induced $emf$ will oppose the main battery $emf$ of $10 \, V$.Therefore,the resultant $emf = 10 \, V - 1 \, V = 9 \, V$.

List-$I$	List-$II$
$A$. Magnetic induction	$I$. $MLT^{-2}A^{-2}$
$B$. Magnetic flux	$II$. $ML^2T^{-2}A^{-2}$
$C$. Magnetic permeability	$III$. $ML^0T^{-2}A^{-1}$
$D$. Self inductance	$IV$. $ML^2T^{-2}A^{-1}$

Similar Questions

The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced currents in wires $AB$ and $CD$ are

Match the List-$I$ with List-$II$:
List-$I$ List-$II$
$A$. Magnetic induction $I$. $MLT^{-2}A^{-2}$
$B$. Magnetic flux $II$. $ML^2T^{-2}A^{-2}$
$C$. Magnetic permeability $III$. $ML^0T^{-2}A^{-1}$
$D$. Self inductance $IV$. $ML^2T^{-2}A^{-1}$

Choose the correct answer from the options given below:

The figure shown has two coils of wires placed in close proximity. The current in primary coil $P$ is made to vary with time as shown in the graph. Which of the following graphs best represents the variation of the emf induced in the secondary coil $S$?

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