Magnetics

A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

Two long conductors, separated by a distance $d$ carry current ${I_1}$ and ${I_2}$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is

Two thin, long, parallel wires, separated by a distance $'d'$ carry a current of $'i'$ $A$ in the same direction. They will

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75^o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30^o with this field. The magnitude of the other field (in mT ) is close to

A magnetic dipole in a constant magnetic field has :

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is :

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :

A charged particle carrying charge 1 $\mu$C is moving with velocity $\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$ ms^–1. If an external magnetic field of $\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$× 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 :