A positive charge is moving towards an observer. The direction of magnetic induction lines is 

A thin ring of radius R metre has charge q coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of f revolutions/s. The value of magnetic field induction in Wb/m² at the centre of the ring is 

A circular coil carrying current behaves as a

A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x>0 is now bent so that it now lies in the y-z plane.

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude

The magnetic field of earth can be modeled by that of a point dipole placed at the center of the earth. The dipole axis makes an angle of \(11.3°\)with the axis of the earth. At Mumbai, declination is nearly zero. Then,

A paramagnetic sample shows a net magnetization of when placed \(8{ Am }^{ -1 }\) in an external magnetic field 0.6 T at a temperature of 4K. When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K, the magnetization will be 

Two particles X and Y having equal charges after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii \({ R }_{ 1 }\quad and\quad { R }_{ 2 }\) respectively. The ratio of the mass of X to that Y is

An electron of mass \({ M }_{ e },\) initially at rest, moves through a certain distance in a uniform electric field in time \({ t }_{ 1 }.\) A proton of mass \({ M }_{ p }\) also initially at rest, takes time \({ t }_{ 2 }\) to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio \({ t }_{ 2 }/{ t }_{ 1 }\) is nearly equal to 

A magnetic needle suspended parallel to a magnetic field requires \(\sqrt { 3 } J\) of work to turn it through \({ 60 }^{ ° }.\) The torque needed to maintain the needle in this position will be :

What are the dimensions of \({ \mu }_{ o }/4\pi \) ?

How will the magnetic field strength at the centre of the circular coil carrying current change, if the current through the coil is doubled and the radius of the coil is halved?

Is the source of magnetic field analogue to the source of electric current.

Write the relation for the force \(\overset { \rightarrow }{ F } \) acting on a charge carrier q moving with a velocity \(\overset { \rightarrow }{ v } \) through a magnetic field \(\overset { \rightarrow }{ B } \)  in vector notation. Using this relation, deduce the conditions under which this force will be (i) maximum (ii) minimum.

a wire of length L is bent round in the form of a coil having N turns of same radius. If a steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its centre.

A charged particle is moving on a circular path of radius R in a uniform magnetic field under the Lorentz force F. How much work is done by the force in one round? Is the momentum of the particle changing?

A rectangular coil of sides l and b carrying a current I is subjected to a uniform magnetic field \(\overset { \rightarrow }{ B } \) acting at an angle \(\theta \)  to its plane. Write the expression for the torque acting on it. In which orientation of the coil in the magnetic field, the torque is (i) minimum and (ii) maximum.

(a) What is the importance of a radical magnetic field and how is it produced?
(b) Why is it that while using a moving coil galvanometer as a voltmeter, a high resistance in series is required whereas in an ammeter a shunt is used?
(c) With the help of a diagram, explain the principle and working of a moving coil galvanometer.

A magnetic field set up using Helmholts coils( described in Exercise ) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of(single-species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is \(9.0\times { 10 }^{ -5 }{ Vm }^{ -1 }\), make a simple guess as to what the beam contains. Why is the answer not unique?

A long horizontal rigidly supported wire carries \({ i }_{ a }\)of 100 A. Directed above it and parallels to it is a fine wire that carries a current \({ i }_{ a }\)of 20A and weighs 0.073N/m. How far above the lower wire should the second wire be kept if we wish to support it by magnetic repulsion?
Given permeability constant \({ \mu }_{ 0 }=4\pi \times { 10 }^{ -7 } \ Wb\ { A }^{ -1 }{ m }^{ -1 }\)

A domain in ferromagnetic iron is in the form of a cube of side length\(1\mu m\).Estimate the number of iron atoms in the domain and the maximum possible dipole moment and magnetisation of the domain.The molecular mass of iron is 55g/mole and its density is\(7.9g/{ cm }^{ 3 }\) .Assume that each iron atom has a dipole moment of\(9.27\times { 10 }^{ -24 }{ Am }^{ 2 }\)

The electron of hydrogen atom moves along a circular path of radius 0.5 x 10^-10 m
(i) with a speed of 4.0 x 10⁶ ms^-1.
(ii) with a frequency 6.8 x 10¹⁵ Hz.
Calculate the magnetic field produced at the centre of the cuircular path. (e = 1.6x10^-19C)

An electric current is flowing in circular coil of radius a.  At what distance from the centre on the axis of the coil will the magnetic field be \(\cfrac { 1 }{ 8 } \) th of its value at the centre?

Assume the dipole model for earth's magnetic field B which by \({ B }_{ v }=\)vertical component of magnetic field = \(\frac { { \mu }_{ 0 } }{ 4\pi } \frac { 2M\cos { \theta } }{ { r }^{ 3 } } { B }_{ H }=\) Horizontal component of magnetic field = \(\frac { { \mu }_{ 0 } }{ 4\pi } \frac { 2M\sin { \theta M } }{ { r }^{ 3 } } ,\theta ={ 90 }^{ \circ }=\) lattitude as measured from magnetic equator. Find loci of points for which
(i) \(\left| B \right| \) is minimum
(ii) dip angle is zero and
(iii) dip angle is\(\pm { 45 }^{ \circ }\).

A long straight conductor C carrying a current of 3 A is placed parallel to a short conductor D of length 5 cm, carrying a current 4 A. The two conductors are 10 cm apart. Find
(i) the magnetic field due to C at D.
(ii) The approximate force on D.