1
JEE Advanced 2014 Paper 2 Offline
+3
-1

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter clockwise direction if seen from above.

Consider d >> a, and the loop is rotated about its diameter parallel to the wires by 30$$^\circ$$ from the position shown in the below figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

A
$${{{\mu _0}{I^2}{a^2}} \over d}$$
B
$${{{\mu _0}{I^2}{a^2}} \over {2d}}$$
C
$${{\sqrt 3 {\mu _0}{I^2}{a^2}} \over d}$$
D
$${{\sqrt 3 {\mu _0}{I^2}{a^2}} \over {2d}}$$
2
JEE Advanced 2013 Paper 2 Offline
+3
-1

A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
A
$${{BR} \over 4}$$
B
$${{BR} \over 2}$$
C
BR
D
2BR
3
JEE Advanced 2013 Paper 2 Offline
+3
-1

A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

A
$$- \gamma BQ{R^2}$$
B
$$- \gamma {{BQ{R^2}} \over 2}$$
C
$$\gamma {{BQ{R^2}} \over 2}$$
D
$$\gamma BQ{R^2}$$
4
IIT-JEE 2012 Paper 2 Offline
+3
-1

A loop carrying current $$l$$ lies in the xy-plane as shown in the figure. The unit vector $$\widehat k$$ is coming out of the plane of the paper. The magnetic moment of the current loop is

A
$${a^2}I\widehat k$$
B
$$\left( {{\pi \over 2} + 1} \right){a^2}I\widehat k$$
C
$$- \left( {{\pi \over 2} + 1} \right){a^2}I\widehat k$$
D
$$(2\pi + 1){a^2}I\widehat k$$
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