A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction is parallel to the axis along east to west.  A wire carrying current of 7.0 A in the north to south direction passes through this region.  What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-southwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil.  If the current in the coil is 5.0 A, what is the 
(a) total torque on the coil,
(b) total force on the coil,  
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10^-5 m², and the free electron density in copper is given to be about 10²⁹ m^-3)

A long straight horizontal cable carries a current of 2.5A in the direction 10^o south of west to 10^o north of east. The magnetic meridian of the place happens to be 10^o west of the geographic meridian, The earth's magnetic field at the location is 0.33G, and the angle of dip is zero. Locate the line of neutral points(Ignore the thickness of the cable).

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12cm. The coil is in a vertical plane making an angle of 45^o with the magnetic meridian. When the current in the coil is 0.35A, the needle points west to east
(a) Determine the horizontal component of the earth's magnetic field at the location.
(b) The current in the coil is reserved and the coil is rotated about its vertical axis by an angle of 90^o in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the place to be zero.

A closely wound solenoid of 2000 turns and area of cross-section 1.6 x 10^-4m² carrying a current of 4.0A is suspended through its centre allowing it to turn in a horizontal plane.
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 x 10^-2T is set up at an angle of 30^o with the axis of the solenoid?

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction.Null points are found on the axis of the magnet at 14 cm from the centre of the magnet.The earth's magnetic field at the place is 0.36 G and the angle of dip is zero.What is the total magnetic field on the normal bisector of the magnet at the same distance as the null point(i.e. 14 cm from the centre of the magnet)?

A sample of paramagnetic salt contains \(2.0\times { 10 }^{ 24 }\)atomic dipoles each of dipole moment \(1.5\times { 10 }^{ -34 }{JT}^{-1}\)The sample is placed under a homogeneous magnetic field of 0.84 Tand cooled to a temperature of 4.2 K.The degree of magnetic saturation achieved is equal to 15.8.What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K?(Assume Curie's law).

Two concentric circular coils X and Y of radii 16 cm and 10 cm respectively lie in the same vertical plane containing the north-south direction. Coil X has 20 turns and carries a current of 16 A ; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise and in Y is clockwise, for an observer looking at the coil facing west. Give the magnitude and direction of the coils at their centre.

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 short bar magnet placed with its axis at \(30°\)to a uniform magnetic field of 0.2T experiences a torque of 0.06Nm.
(i) Calculate magnetic moment of the magnet and 
(ii) Find out what orientation of the magnet corresponds to a stable equilibrium in the magnetic field.

An iron sample having mass 8.4 kg is repeatedly taken over cycles of magnetisation and demagnetization at a frequency of 50Hz.It is found that energy of 3.2 J is dissipated as heat in the sample in 30 minutes. If the density of iron is \(7200kg{ m }^{ -3 }\) calculate the value of energy dissipated per unit volume per cycle in the iron sample. 

While watching Discovery channel Sheela was impressed that certain organisms have the ability to sense the field lines of earth's magnetic field. They use this ability to travel from one location to another, Sheela wanted to find the angle of dip at her place. She then mounted the compass on a cardboard and placed it vertically along the magnetic meridian. She was able to measure the angle of dip
(a) What values did Sheela have?
(b) Define the magnetic element of earth.

What is te magnitude of the equatorial and axial fields due to a bar magnet of length 5.0 cm at a distance of 50 cm from its mid-point? The magnetic moment of the bar magnet is \(0.40{ Am }^{ 2 }\)

Calculate the magnetic field \(\vec { B } \) at a distance 0.1 from a long straight wire carrying a current of 5A.