Induced Electromotive Force
PHXII06:ELECTROMAGNETIC INDUCTION

358504 There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate \(dB/dt\) as shown in figure. A charged particle having charge \(q\) and mass \(m\) is kept in equilibrium, at the top of a spring of spring constant \(K\), in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be
supporting img

1 \(\dfrac{1}{K}\left[m g+\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
2 \(\dfrac{1}{K}\left[m g+\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
3 \(\dfrac{1}{K}\left[m g-\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
4 \(\dfrac{1}{K}\left[m g-\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
PHXII06:ELECTROMAGNETIC INDUCTION

358505 Assertion :
Situations of induced electric field due to changing magnetic flux are more readily observed than situations of induced magnetic field due to changing electric flux.
Reason :
The phenomenon of induction of either field is not linked to flux.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358506 A magnetic field \(B=C_{1} t+C_{2}\) is directed into the plane of paper in the cylindrical volume of radius ' \(r\) '. Here \(C_{1}\) and \(C_{2}\) are positive constants and '\(t\) ' is in seconds. A loop is in the form of an equilateral triangle ' \(ABC\) ' of side length ' \(2r\) ' is placed such that vertex \(C\) lies on the axis of cylindrical region and the plane of loop is perpendicular to the axis. Resistance of unit length of wire is ' \(\lambda\) ' \(\Omega / m\). Find the emf across \(AB\) after some time \(t\).
supporting img

1 \(\dfrac{C_{1} \pi r^{2}}{6}\)
2 \(\dfrac{C_{1} \pi r^{2}}{3}\)
3 \(\dfrac{C_{1} \pi r^{2}}{2}\)
4 \(\dfrac{C_{1} \pi r^{2}}{9}\)
PHXII06:ELECTROMAGNETIC INDUCTION

358507 As a result of change in magnetic flux linked to the closed loop shown in figure, an emf \(V\) volt is induced in the loop. The work done in taking a charge \(Q\) coulomb once along the loop is
supporting img

1 \(QV\)
2 \(QV/2\)
3 \(2QV\)
4 Zero
PHXII06:ELECTROMAGNETIC INDUCTION

358508 Assertion :
The work done by a charge in a closed loop of induced current is non-zero.
Reason :
Induced electric field is non-conservative in nature.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358504 There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate \(dB/dt\) as shown in figure. A charged particle having charge \(q\) and mass \(m\) is kept in equilibrium, at the top of a spring of spring constant \(K\), in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be
supporting img

1 \(\dfrac{1}{K}\left[m g+\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
2 \(\dfrac{1}{K}\left[m g+\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
3 \(\dfrac{1}{K}\left[m g-\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
4 \(\dfrac{1}{K}\left[m g-\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
PHXII06:ELECTROMAGNETIC INDUCTION

358505 Assertion :
Situations of induced electric field due to changing magnetic flux are more readily observed than situations of induced magnetic field due to changing electric flux.
Reason :
The phenomenon of induction of either field is not linked to flux.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358506 A magnetic field \(B=C_{1} t+C_{2}\) is directed into the plane of paper in the cylindrical volume of radius ' \(r\) '. Here \(C_{1}\) and \(C_{2}\) are positive constants and '\(t\) ' is in seconds. A loop is in the form of an equilateral triangle ' \(ABC\) ' of side length ' \(2r\) ' is placed such that vertex \(C\) lies on the axis of cylindrical region and the plane of loop is perpendicular to the axis. Resistance of unit length of wire is ' \(\lambda\) ' \(\Omega / m\). Find the emf across \(AB\) after some time \(t\).
supporting img

1 \(\dfrac{C_{1} \pi r^{2}}{6}\)
2 \(\dfrac{C_{1} \pi r^{2}}{3}\)
3 \(\dfrac{C_{1} \pi r^{2}}{2}\)
4 \(\dfrac{C_{1} \pi r^{2}}{9}\)
PHXII06:ELECTROMAGNETIC INDUCTION

358507 As a result of change in magnetic flux linked to the closed loop shown in figure, an emf \(V\) volt is induced in the loop. The work done in taking a charge \(Q\) coulomb once along the loop is
supporting img

1 \(QV\)
2 \(QV/2\)
3 \(2QV\)
4 Zero
PHXII06:ELECTROMAGNETIC INDUCTION

358508 Assertion :
The work done by a charge in a closed loop of induced current is non-zero.
Reason :
Induced electric field is non-conservative in nature.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358504 There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate \(dB/dt\) as shown in figure. A charged particle having charge \(q\) and mass \(m\) is kept in equilibrium, at the top of a spring of spring constant \(K\), in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be
supporting img

1 \(\dfrac{1}{K}\left[m g+\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
2 \(\dfrac{1}{K}\left[m g+\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
3 \(\dfrac{1}{K}\left[m g-\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
4 \(\dfrac{1}{K}\left[m g-\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
PHXII06:ELECTROMAGNETIC INDUCTION

358505 Assertion :
Situations of induced electric field due to changing magnetic flux are more readily observed than situations of induced magnetic field due to changing electric flux.
Reason :
The phenomenon of induction of either field is not linked to flux.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358506 A magnetic field \(B=C_{1} t+C_{2}\) is directed into the plane of paper in the cylindrical volume of radius ' \(r\) '. Here \(C_{1}\) and \(C_{2}\) are positive constants and '\(t\) ' is in seconds. A loop is in the form of an equilateral triangle ' \(ABC\) ' of side length ' \(2r\) ' is placed such that vertex \(C\) lies on the axis of cylindrical region and the plane of loop is perpendicular to the axis. Resistance of unit length of wire is ' \(\lambda\) ' \(\Omega / m\). Find the emf across \(AB\) after some time \(t\).
supporting img

1 \(\dfrac{C_{1} \pi r^{2}}{6}\)
2 \(\dfrac{C_{1} \pi r^{2}}{3}\)
3 \(\dfrac{C_{1} \pi r^{2}}{2}\)
4 \(\dfrac{C_{1} \pi r^{2}}{9}\)
PHXII06:ELECTROMAGNETIC INDUCTION

358507 As a result of change in magnetic flux linked to the closed loop shown in figure, an emf \(V\) volt is induced in the loop. The work done in taking a charge \(Q\) coulomb once along the loop is
supporting img

1 \(QV\)
2 \(QV/2\)
3 \(2QV\)
4 Zero
PHXII06:ELECTROMAGNETIC INDUCTION

358508 Assertion :
The work done by a charge in a closed loop of induced current is non-zero.
Reason :
Induced electric field is non-conservative in nature.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358504 There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate \(dB/dt\) as shown in figure. A charged particle having charge \(q\) and mass \(m\) is kept in equilibrium, at the top of a spring of spring constant \(K\), in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be
supporting img

1 \(\dfrac{1}{K}\left[m g+\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
2 \(\dfrac{1}{K}\left[m g+\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
3 \(\dfrac{1}{K}\left[m g-\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
4 \(\dfrac{1}{K}\left[m g-\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
PHXII06:ELECTROMAGNETIC INDUCTION

358505 Assertion :
Situations of induced electric field due to changing magnetic flux are more readily observed than situations of induced magnetic field due to changing electric flux.
Reason :
The phenomenon of induction of either field is not linked to flux.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358506 A magnetic field \(B=C_{1} t+C_{2}\) is directed into the plane of paper in the cylindrical volume of radius ' \(r\) '. Here \(C_{1}\) and \(C_{2}\) are positive constants and '\(t\) ' is in seconds. A loop is in the form of an equilateral triangle ' \(ABC\) ' of side length ' \(2r\) ' is placed such that vertex \(C\) lies on the axis of cylindrical region and the plane of loop is perpendicular to the axis. Resistance of unit length of wire is ' \(\lambda\) ' \(\Omega / m\). Find the emf across \(AB\) after some time \(t\).
supporting img

1 \(\dfrac{C_{1} \pi r^{2}}{6}\)
2 \(\dfrac{C_{1} \pi r^{2}}{3}\)
3 \(\dfrac{C_{1} \pi r^{2}}{2}\)
4 \(\dfrac{C_{1} \pi r^{2}}{9}\)
PHXII06:ELECTROMAGNETIC INDUCTION

358507 As a result of change in magnetic flux linked to the closed loop shown in figure, an emf \(V\) volt is induced in the loop. The work done in taking a charge \(Q\) coulomb once along the loop is
supporting img

1 \(QV\)
2 \(QV/2\)
3 \(2QV\)
4 Zero
PHXII06:ELECTROMAGNETIC INDUCTION

358508 Assertion :
The work done by a charge in a closed loop of induced current is non-zero.
Reason :
Induced electric field is non-conservative in nature.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358504 There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate \(dB/dt\) as shown in figure. A charged particle having charge \(q\) and mass \(m\) is kept in equilibrium, at the top of a spring of spring constant \(K\), in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be
supporting img

1 \(\dfrac{1}{K}\left[m g+\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
2 \(\dfrac{1}{K}\left[m g+\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
3 \(\dfrac{1}{K}\left[m g-\dfrac{2 q R^{2}}{\ell} \dfrac{d B}{d t}\right]\)
4 \(\dfrac{1}{K}\left[m g-\dfrac{q R^{2}}{2 \ell} \dfrac{d B}{d t}\right]\)
PHXII06:ELECTROMAGNETIC INDUCTION

358505 Assertion :
Situations of induced electric field due to changing magnetic flux are more readily observed than situations of induced magnetic field due to changing electric flux.
Reason :
The phenomenon of induction of either field is not linked to flux.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII06:ELECTROMAGNETIC INDUCTION

358506 A magnetic field \(B=C_{1} t+C_{2}\) is directed into the plane of paper in the cylindrical volume of radius ' \(r\) '. Here \(C_{1}\) and \(C_{2}\) are positive constants and '\(t\) ' is in seconds. A loop is in the form of an equilateral triangle ' \(ABC\) ' of side length ' \(2r\) ' is placed such that vertex \(C\) lies on the axis of cylindrical region and the plane of loop is perpendicular to the axis. Resistance of unit length of wire is ' \(\lambda\) ' \(\Omega / m\). Find the emf across \(AB\) after some time \(t\).
supporting img

1 \(\dfrac{C_{1} \pi r^{2}}{6}\)
2 \(\dfrac{C_{1} \pi r^{2}}{3}\)
3 \(\dfrac{C_{1} \pi r^{2}}{2}\)
4 \(\dfrac{C_{1} \pi r^{2}}{9}\)
PHXII06:ELECTROMAGNETIC INDUCTION

358507 As a result of change in magnetic flux linked to the closed loop shown in figure, an emf \(V\) volt is induced in the loop. The work done in taking a charge \(Q\) coulomb once along the loop is
supporting img

1 \(QV\)
2 \(QV/2\)
3 \(2QV\)
4 Zero
PHXII06:ELECTROMAGNETIC INDUCTION

358508 Assertion :
The work done by a charge in a closed loop of induced current is non-zero.
Reason :
Induced electric field is non-conservative in nature.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.