Magnetic Dipole in External Magnetic Field

A circular coil of $25$ turns and radius of $12 \mathrm{cm}$ is placed in a uniform magnetic field of $0.5 \mathrm{T}$ normal to the plane of coil. If the current in the coil is $5 \mathrm{A}$, then total torque experienced by the coil is

A square loop of side $a$ is made up of a metallic wire carrying a current $I$. The loop is kept perpendicular to a uniform magnetic field. Now the shape of the loop is changed from square to a circle without changing the length of the wire and current. The amount of work done in doing so is:

A magnet is placed in earth's magnetic field with north pole of the magnet pointing north. At the neutral point 

The work done in rotating a bar magnet of magnetic moment $\mathrm{M}$ from its unstable equilibrium position to its stable equilibrium position in a uniform magnetic field is $\mathrm{B}$is

Two magnetic are as shown in figure. Force between them is

The short bar magnetic are placed as shown in figure. The magnetic of force between them is proportional to

If two short bar magnetic are placing the line joining then as shown in the figure. Nature of force between two magnetic is

An electron moves in a circular orbit with a uniform speed $v.$ It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to :

A bar magnet of length $10 \mathrm{cm}$ and pole strength $2\mathrm{Am}$ is making an angle $60°$ with a uniform magnetic field of induction $50 T.$ Then the couple acting on it is ____ $\mathrm{Nm}$

Two short bar magnets each of magnetic moment $9 {\mathrm{Am}}^2$ are placed such that one is at $x=-3 \mathrm{cm}$ and the other at $y=-3 \mathrm{cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively then the resultant magnetic field at the origin is

A magnetic needle of magnetic moment $2\pi \times {10}^{-2}{\mathrm{Am}}^2$ and moment of inertia $\frac{4}{\pi }\times {10}^{-6} \mathrm{kg} {\mathrm{m}}^2$ is performing simple harmonic oscillations in a magnetic field of $0.02 \mathrm{T}.$ Time taken for $10$ complete oscillations is :

The effect on a freely suspended magnetic needle due to a uniform magnetic field is as follow.

A magnet makes $40$ oscillations per minute at a place having earth's horizontal magnetic field intensity of $0.1\times {10}^{-5} \mathrm{T}$. At another place, it takes $2.5 \mathrm{s}$  to complete one vibration. The value of earth's horizontal field at that place is

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

The curve that may best represent the current vs deflection in a tangent galvanometer is

Consider two short magnets $A$ and $B$ whose lengths are in $1:2$ ratio and the pole strength are in $1:3$ ratio. The magnet produces a $30°$ deflection when placed at a certain distance in $\tan A$ position of the magnetometer. If the magnet $B$ is placed at the same distance in $\tan B$ position of the magnetometer, then find the deflection produced:

A magnetic dipole is under the influence of two magnetic fields. The angle between the field direction is $60°$ and one of the fields has a magnitude of $1.2\times {10}^{-2}$ T. If the dipole comes to stable equilibrium at an angle of $30°$ with this field, then the magnitude of the field is

A bar magnet of magnetic moment $1.5 \mathrm{J }{\mathrm{T}}^{-1}$ lies aligned with the direction of a magnetic field of $0.22 \mathrm{T}.$ What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction?

There is a hoop and solid cylinder of same mass and same dimensions. The magnetic moment of hoop of double of cylinder. Now both hoop and cylinder are oscillated in uniform magnetic field then the relation between time period of hoop & cylinder is

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy.