Effect of a Uniform Magnetic Field on a Current Loop

A rectangular coil PQ has $2n$ turns, an area $2a$ and carries a current $2I$, (refer figure). The plane of the coil is at $60^{\text{o}}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

A conducting ring of mass $2 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ is placed on a smooth horizontal plane. The ring carries a current $i=4 \mathrm{A}$. A horizontal magnetic field $B=10 \mathrm{T}$ is switched on at time $t=0$ as shown in the figure. The initial angular acceleration of the ring will be

A cone made of insulating material has a total charge $\mathit{Q}$ spread uniformly over its sloping surface having a slant length $\mathit{L}$. The energy required to take a test charge $\mathit{q}$ from infinity to apex $\mathrm{A}$ of the cone will be
 

A wire loop carrying current $i$ is placed in the $x-y$ plane as shown in the figure. If an external uniform magnetic field $\overrightarrow{B}=B\hat{\text{i}}$ is switched on, then the torque acting on the loop is

A square current carrying loop made of thin wire and having a mass m = 10g can rotate without friction with respect to the vertical axis $\mathrm{{\rm O}}{\mathrm{{\rm O}}}_1\text{,}$passing through the centre of the loop at right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $\text{B}={\text{10}}^{-1}\text{T}$directed at right angles to the plane of the drawing. A current I = 2A is flowing in the loop. Find the period of small oscillations that the loop performs about its position of stable equilibrium.

   

A uniform rigid square wire frame of side length $l$ and mass $4m$ is placed on a smooth horizontal surface where exists a uniform horizontal magnetic field of Intensity $B$. Now current that is double of minimum current required to flip over the frame is switched on in the coil. Then just after current is switched on

The magnetic field at the centre of a current carrying loop of radius $0.1 \mathrm{m}$ is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the centre of the loop is(in $\mathrm{cm}$)

The magnetic needle of a vibration magnetometer makes 12 oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line, it makes 15 oscillations per minute. If the poles of the bar magnet are interchanged, the number of oscillations it makes per minute is $\sqrt{n}$. What is the value of $n$?

A wire loop $ABCDEA$ carrying a current $I$ is placed in $X-Y$ plane as shown. The external magnetic field $\overrightarrow{B}=B_x\hat{i}+B_z\hat{k}$ is applied in the region(here $B_{\mathrm{x}}$ and $B_{\mathrm{z}}$ are constant). Then if torque acting on the loop is $\frac{i{r}^2}{k}\left(\pi -1\right)B_x$ find $k$.

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3} \mathrm{J}$ of work to turn it through $60°$. The torque needed to maintain the needle in this position will be

The magnetic field at the centre of a current carrying loop of radius 0.1 m is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the centre of the loop is

Calculate the couple (in $\mu \mathrm{N} \mathrm{m}$) acting on a magnet of length $10 \mathrm{cm}$ and pole strength $15 \mathrm{A} \mathrm{m}$, kept in a field of $B=2\times {10}^{-5} \mathrm{T}$ at an angle of $30°$.

The following statement is false for Helmholtz coils:

A magnet of magnetic moment $M$ is situated with its axis along the direction of a magnetic field of strength $B$. The work done in rotating it by an angle of $180°$ will be

A wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. If this coil is placed in a magnetic field, then the torque acting on the coil will be maximum when the number of turns is

A coil in the shape of an equilateral triangle of side $0.02 \mathrm{m}$ is suspended from its vertex, such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a uniform field of $5\times {10}^{-2} \mathrm{T}.$ If a current of $0.1 \mathrm{A}$ is passed through the coil, what is the couple acting?

A magnet of magnetic moment $50\hat{\mathrm{i}} \mathrm{A} {\mathrm{m}}^2$ is placed along the $X$-axis in a magnetic field $\overrightarrow{\mathrm{B}}=\left(0.5\hat{\mathrm{i}}+3.0\hat{\mathrm{j}}\right) \mathrm{T}$. The torque acting on the magnet is :-

A current carrying loop is free to turn in a uniform magnetic field. The loop will then come into equilibrium when its plane is inclined at

Four wires, of equal length, are bent in the form of four loops, $P, Q, R$ and $S$. They are suspended in a uniform magnetic field and same current is passed through them. The maximum torque will act on

A circular loop with $N$ turns has radius $r$. It lies in x-y plane carrying current $I$ in anti-clockwise direction. If the magnetic field in the region is $\overrightarrow{B}=B_0\widehat{i},$ then find the torque $\left(\overrightarrow{\tau }\right)$ acting on the loop.