Three harmonic waves having equal frequency $$\nu$$ and same intensity $$I_0$$, have phase angles 0, {\pi \over 4} and - {\pi \over 4} respectively. When they are superimposed the intensity of the resultant wave is close to :

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v0 = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 $$\times$$ 1011 Nm-2, the extension of wire over its natural length is :

A square loop of side 2$$a$$ and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be :

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $$\overrightarrow{B}$$. The magnetic moment of this moving particle:

A particle of charge q and mass m is moving with a velocity $$-v\hat{i}$$ (v $$\ne$$ 0) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $$\overrightarrow{B}=B_0\hat{k}$$ , the maximum value of v for which the particle will not hit the screen is :

An electron is moving along +x direction with a velocity of 6 $$\times$$ 106 ms–1. It enters a region of uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be :

An iron rod of volume 10–3 m3 and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be :

A square loop of side 2$$a$$, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about zaxis is given by :

A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2 . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o will be:

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of {{{\mu _0}I} \over \pi } is :

A charged particle carrying charge 1 $$\mu$$C is moving with velocity $$\left(2\hat{i}+3\hat{j}+4\hat{k}\right)$$ ms–1. If an external magnetic field of $$\left(5\hat{i}+3\hat{j}-6\hat{k}\right)$$× 10–3 T exists in the region where the particle is moving then the force on the particle is $$\overrightarrow{F}$$ × 10–9 N. The vector $$\overrightarrow{F}$$ is :

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the centre of circle is :

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

A particle of mass m and charge q has an initial velocity $$\overrightarrow{v}=v_0\hat{j}$$ . If an electric field $$\overrightarrow{E}=E_0\hat{i}$$ and magnetic field $$\overrightarrow{B}=B_0\hat{i}$$ act on the particle, its speed will double after a time:

Photon with kinetic energy of 1MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is 1.6 × 10–27 kg) :

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance {a \over 3} and 2$$a$$, respectively from the axis of the wire is :

A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $$E\overrightarrow{i}$$ and a uniform magnetic field $$B\overrightarrow{k}$$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $$v\overrightarrow{i}$$ and $$-2v\overrightarrow{j}$$ . Then which of the following statements (A, B, C, D) are the correct ? (Trajectory shown is schematic and not to scale) : (A) E = {3 \over 4}\left( {{{m{v^2}} \over {qa}}} \right) (B) Rate of work done by the electric field at P is {3 \over 4}\left( {{{m{v^3}} \over a}} \right) (C) Rate of work done by both the fields at Q is zero (D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav.

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning) :