Moving Charges and Magnetism

A proton, an electron and an $\alpha$-particle enter at right angles to a uniform magnetic field with the same velocity. If $R_p, R_e$ and $R_\alpha$ are the radii of circular paths of these particles, then

Biot-Savart law indicates that an electron moving with a velocity $\vec{V}$ produces a magnetic field $\vec{B}$ around it such that

Two identical circular current loops carrying equal currents are placed with their axes inclined at $45^\circ$ to each other as shown in the figure. The resultant magnetic field at P is

A point charge is placed in a moving train. A passenger A sitting in the train and person B on the ground observe the fields due to this charge. Then

Which of the following graphs represents the variation of magnetic field $B$ with perpendicular distance ' $r$ ' from an infinitely long, straight conductor carrying current?

Two thin long parallel wires separated by a distance ' $r$ ' from each other in vacuum carry a current of I ampere in opposite directions. Then, they will

A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 7A. The magnetic field at the centre of the solenoid is

A square loop of side 2 m lies in the Y-Z plane in a region having a magnetic field $\overrightarrow{\mathrm{B}}=(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \mathrm{T}$. The magnitude of magnetic flux through the square loop ...

Identify the correct statement

A uniform magnetic field of strength $B=2 \mathrm{mT}$ exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere $S_1$, a right circular cone $S...

19. A particle of specific charge $q / m=\pi \mathrm{C} \mathrm{kg}^{-1}$ is projected the origin towards positive $X$-axis with the velocity $10 \mathrm{~ms}^{-1}$ in a uniform magnetic field $\mathbf{B}=-2 \hat{\mathbf{k} T}$. The velocit...

A coil having 9 turns carrying a current produces magnetic field $B_1$ at the centre. Now the coil is rewounded into 3 turns carrying same current. Then, the magnetic field at the centre $B_2=$

A moving electron produces

The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is 64 times the magnetic field at a distance $x$ on its axis from the centre of the coil. Then, the value of $x$ is

A proton and an alpha-particle moving with the same velocity enter a uniform magnetic field with their velocities perpendicular to the magnetic field. The ratio of radii of their circular paths is

The torque acting on a magnetic dipole placed in uniform magnetic field is zero, when the angle between the dipole axis and the magnetic field is .........

A positively charged particle \(q\) of mass $m$ is passed through a velocity selector. It moves horizontally rightward without deviation along the line \(y=\frac{2 m v}{q B}\) with a speed \(v\). The electric field is vertically downwards a...

A charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes increase in its speed

Which of the following statements proves that Earth has a magnetic field ?

A circular coil of wire of radius \(r\) has \(n\) turns and carries a current \(I\). The magnetic induction \(B\) at a point on the axis of the coil at a distance \(\sqrt{3} r\) from its centre is

A solenoid of length \(50 \mathrm{~cm}\) having 100 turns carries a current of \(2.5 \mathrm{~A}\). The magnetic field at one end of the solenoid is

A proton moves with a velocity of \(5 \times 10^6 \hat{\mathbf{\widehat j} m \mathrm{~m}^{-1}}\) through the uniform electric field,
$$\mathbf{\overrightarrow E}=4 \times 10^6[2 \hat{\mathbf{i}}+0.2 \hat{\mathbf{j}}+0.1 \hat{\mathbf{k}}] \...

A metallic rod of mass per unit length \(0.5 \mathrm{~kg} \mathrm{~m}^{-1}\) is lying horizontally on a smooth inclined plane which makes an angle of \(30^{\circ}\) with the horizontal. A magnetic field of strength \(0.25 \mathrm{~T}\) is a...

A toroid with thick windings of \(N\) turns has inner and outer radii \(R_1\) and \(R_2\), respectively. If it carries certain steady current \(I\), the variation of the magnetic field due to the toroid with radial distance is correctly gra...

Which of the field pattern given below is valid for electric field as well as for magnetic field?

A tightly wound long solenoid has $n$ turns per unit length, a radius \(r\) and carries a current \(I\). A particle having charge \(q\) and mass \(m\) is projected from a point on the axis in a direction perpendicular to the axis. The maxim...

Two parallel wires in free space are \(10 \mathrm{~cm}\) apart and each carries a current of \(10 \mathrm{~A}\) in the same direction. The force exerted by one wire on the other [per unit length] is

A strong magnetic field is applied on a stationary electron. Then, the electron

A copper rod \(A B\) of length \(l\) is rotated about end \(A\) with a constant angular velocity \(\omega\). The electric field at a distance \(x\) from the axis of rotation is

Two long straight parallel wires are a distance \(d\) part. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field $B$ along the line \(x x^{\prime}\) is given by

A long cylindrical wire of radius \(R\) carries a uniform current \(I\) flowing through it. The variation of magnetic field with distance \(r\) from the axis of the wire is shown by

In the given figure, the magnetic field at \(O\).

The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is \(x\), if the current and the radius both are doubled. The new ratio will become

The magnetic field at the origin due to a current element \(i d \mathbf{l}\) placed at a point with vector position \(\mathrm{r}\) is

A cyclotron is used to accelerate protons \(\left({ }_1^l \mathrm{H}\right)\) deuterons \(\left({ }_1^2 \mathrm{H}\right)\) and \(\alpha\)-particles \(\left({ }_2^4 \mathrm{He}\right)\). While exiting under similar conditions, the minimum $...

The magnetic fields at the centre O in the given figure is

Coersivity of a magnet where the ferromagnet gets completely demagnetized is \(3 \times 10^3 \mathrm{~Am}^{-1}\). The minimum current required to be passes in a solenoid having 1000 turns per metre, so that the magnet gets completely demagn...

The number of turns in a coil of galvanometer is tripled, then

In a cyclotron a charged particle

A toroid has 500 turns per meter length. If it carries a current of \(2 \mathrm{A}\), the magnetic energy density inside the toroid is

An electron is moving in a circle of radius $r$ in a uniform magnetic field $B$. Suddenly, the field is reduced to $\frac{B}{2}$. The radius of the circular path now becomes

A cyclotron's oscillator frequency is 10 MHz and the operating magnetic field is 0.66 T . If the radius of its dees is 60 cm , then the kinetic energy of the proton beam produced by the accelerator is

A charge $q$ is accelerated through a potential difference $V$. It is then passed normally through a uniform magnetic field, where it moves in a circle of radius $r$. The potential difference required to move it in a circle of radius $2 r$ ...

The correct Biot-Savart law in vector form is

A straight wire of length 50 cm carrying a current of 2.5 A is suspended in mid-air by a uniform magnetic field of 0.5 T (as shown in figure). The mass of the wire is ( $g=10 \mathrm{~ms}^{-2}$ )

A magnetic dipole of magnetic moment $6 \times 10^{-2}$ A-m ${ }^2$ and moment of inertia $12 \times 10^{-6} \mathrm{~kg}-\mathrm{m}^2$ performs oscillations in a magnetic field of $2 \times 10^{-2} \mathrm{~T}$. The time taken by the dipol...

A proton, a deuteron and an $\alpha$-particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

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