1
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 2
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
3
IIT-JEE 2011 Paper 2 Offline
+3
-1

A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the xy-plane and a steady current I flows through the wire. The z-component of the magnetic field at the centre of the spiral is A
$${{{\mu _0}NI} \over {2(b - a)}}\ln \left( {{b \over a}} \right)$$
B
$${{{\mu _0}NI} \over {2(b - a)}}\ln \left( {{{b + a} \over {b - a}}} \right)$$
C
$${{{\mu _0}NI} \over {2b}}\ln \left( {{b \over a}} \right)$$
D
$${{{\mu _0}NI} \over {2b}}\ln \left( {{{b + a} \over {b - a}}} \right)$$
4
IIT-JEE 2010 Paper 1 Offline
+3
-1

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is A
IBL
B
$${{IBL} \over \pi }$$
C
$${{IBL} \over {2\pi }}$$
D
$${{IBL} \over {4\pi }}$$
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