1
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
$$\gamma BQ{R^2}$$
2
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
$$(2\pi + 1){a^2}I\widehat k$$
3
IIT-JEE 2012 Paper 2 Offline
+3
-1

An infinite long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, $$\left| {\overrightarrow B } \right|$$ as a function of the radial distance r from the axis is best represented by

A B C D 4
IIT-JEE 2011 Paper 1 Offline
+3
-0.75
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency '$${\omega _p}$$' which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency $$\omega$$, where a part of the energy is absorbed and a part of it is reflected. As $$\omega$$ approaches $${\omega _p}$$ all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N $$\approx$$ 4 $$\times$$ 1027 m-3. Taking $${{\varepsilon _0}}$$ = 10- 11 and m $$\approx$$ 10- 30, where these quantities are in proper SI units.

A
800 nm
B
600 nm
C
300 nm
D
200 nm
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