Two long wires carrying currents I₁ and I₂ are arranged as shown in the figure. One carrying current I₁ is along the X-axis. The other carrying current I₂ is along a line parallel to Y-axis, given by x = 0 and z = d. Find the force exerted at point O₂ because of the wire along the X-axis.

A cyclotron when being used to accelerate positive ions? (Mass = 6.7 x 10^-27kg, charge = 3.2 x 10^-19C) has a magnetic field of ( \(\frac { \pi }{ 2 }\)) T. What must be the value of the frequency of the applied alternating electric field to be used in it?

A current of 5 A is flowing from South to North in a straight wire. Find the magnetic field due to a 1cm piece of wire at a point 1m North-East from the piece of wire.

A short bar magnet has a magnetic moment of 0.48 J/T. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10cm from the centre of the magnet on
(i)  the axis,
(ii) the equatorial lines (normal bisector) of the magnet.

If two magnets having magnetic moments M and M\(\sqrt { 3 } \) are joined to form a cross (i.e. X). The combination is suspended freely in a uniform magnetic field. In equilibrium position, the magnet having magnetic moment M makes an angle \(\theta \) with the field. Calculate the value of \(\theta \)