Do magnetic field obey Newton's third law. Verify for two current elements `vecdl_1=dl hati` located at the origin and `vecdl_2=dl hatj` located at (0, R, 0). Both carry current I.

State the Biot-Savart's law for the magnetic field due to a current carrying element. Use this law to obtain a formula for magnetic field at athe centre of circular loop of radius r carrying steady current I . Sketch the magnetic field lines for a current loop clearly indicating the direction of the field.

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction 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, the wire intersects the axis.

A current of 10 A flow around a closed path in a circuit which is in the horizontal plane as shown in the figure. The circuit consists of eight alternative arcs of radii r_(1)=0.08m and r_(2)=0.12m . Each subtends the same angle at the centre. An infinitely long straight wire carrying a current of 10 A is passing throgh the entre of the above circuit vertically with the direction of the current being into the plane of the circuit. What is the force acting on the wire at the centre due to the current in the circuit? What is the force acting on the arc AC and the straight segment CD due to the current at the centre?

A rectangular loop of sides 8 cm and 2 cm with a cut is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s^-1 . If the cut is joined and the loop has a resistance of 1.6 Omega , how much power is dissipated by the loop as heat? What is the source of this power?

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction 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, the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction 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, the wire is turned from N-S to northeast-northwest direction,

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . The current in the coil in (a) is switched off and the coil s positioned as shown in the figure. The coil is then turned thorugh an angle of 90^@ in a time of 0.14 s. Calculate the average e.m.f. induced in the coil.

The magnetic field at a distance r from a long wire carryimg current I is 0.4 T. The magnetic field at a distance 2r is

Use Biot-Savart's law to obtain the expression for the magnetic field at the centre of a coil in the form of a square of sides 2a carrying a current 'I'.

Calculate the magnetic field due to a circular coil of 250 turns and of diameter 0.1m, carrying a current of 7A at a point on the axis of the coil at a distance 0.12m from the center of the coil.