Magnetic Effects of Current

A hollow, right circular cone of base radius $R$ and height $h$, with its tip at the origin is rotating about the $Z$-axis with an angular velocity $\omega$, as shown in the figure. The cone carries a total charge $Q$ uniformly distributed on its curved surface. The magnitude of magnetic field at a point $(0,0,z)$, where $z\gg R$ and $z\gg h$, is $\dfrac{n\mu_0}{4\pi}\dfrac{QR^2\omega}{z^3}$. The value of $n$ is:

In a vacuum chamber, a particle of charge $1\ \mu$C and mass $1$ mg is projected with a velocity $(\hat\imath+2\hat\jmath)$ ms$^{-1}$ from the $XZ$ plane at time $t=0$ in an electric field of $1\hat\imath$ Vm$^{-1}$. At $t=0.2$ s, the electric field is switched off and a magnetic field of $6\hat\jmath$ T is switched on. The acceleration due to gravity is $-10\hat\jmath$ ms$^{-2}$. Correct option(s) is/are:

As shown in the figure, the resistance of a galvanometer $G$ can be found by the half-deflection method. Here the resistance $R_2$ is adjusted such that when the key $K$ is closed the deflection in the galvanometer becomes half of the value as compared to when $K$ is open. Half-deflection is obtained at $R_2=4\ \Omega$ and thus the galvanometer resistance is found to be $6\ \Omega$. In this half-deflection condition the current (in mA) through the resistor $R_1$ is:

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\dfrac{B_1}{B_2}$ is ________.

An electromagnetic wave travelling in $x$-direction is described by field equation $E_y=300\sin\omega\left(t-\dfrac xc\right)$. If the electron is restricted to move in $y$-direction only with speed of $1.5\times10^6$ m/s then ratio of maximum electric and magnetic forces acting on the electron is ________.

1 μC charge moving with velocity $\vec v=\left(\hat i-2\hat j+3\hat k\right)$ m/s in the region of magnetic field $\vec B=\left(2\hat i+3\hat j-5\hat k\right)$ T. The magnitude of force acting on it is $\sqrt\alpha\times10^{-6}$ N. The value of $\alpha$ is ________.

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4\hat j$ N/C and $4\times10^{-3}\hat k$ T experiences a force of $\left(4\hat i+2\hat j\right)\times10^{-10}$ N. The velocity of the particle at that instant is ________ m/s.

A circular current loop of radius $R$ is placed inside square loop of side length $L$ ($L\gg R$) such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between circular loop and square loop is ________.

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom ________.

An insulated wire is wound so that it forms a flat coil with $N=200$ turns. The radius of the innermost turn is $r_1=3$ cm, and of the outermost turn $r_2=6$ cm. If 20 mA current flows in it then the magnetic moment will be $\alpha\times10^{-2}$ A.m². The value of $\alpha$ is ________.

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 T. The magnetic intensity in SI units is $\alpha\times10^5$. The value of $\alpha$ is ________.
(Free space permeability $\mu_0=4\pi\times10^{-7}$ SI units.)

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of 30° with the direction of the magnetic field. The torque acting on the coil is $\alpha\times10^{-4}$ N.m. The value of $\alpha$ is ________. ($\pi=3.14$)

The charged particle moving in a uniform magnetic field of $\left(3\hat i+2\hat j\right)$ T has an acceleration $\left(4\hat i-\dfrac x2\hat j\right)$ m/s². The value of $x$ is

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec v=\left(\dfrac{v_0}{\sqrt2}\hat x+\dfrac{v_0}{\sqrt2}\hat y\right)$. There exists a uniform magnetic field $\vec B=B_0\hat z$ and a space varying electric field $\vec E=E_0e^{-\lambda x}\hat x$ within the region $0\le x\le L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is ________.

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha\times10^{-14}$ J. The value of $\alpha$ is ________.

($\mu_o=4\pi\times10^{-7}$ Tm/A, $\pi=3.14$)

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is ________ μT.

$\left(\dfrac{\mu_o}{4\pi}=10^{-7}\text{ N/A}^2\right)$

A moving coil of galvanometer when shunted with 2 Ω resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 Ω is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is ________ Ω.

A current carrying circular loop of radius 2 cm with unit normal $\hat n=\dfrac{\hat k+\hat i}{\sqrt2}$ is placed in a magnetic field, $\vec B=B_o\left(3\hat i+2\hat k\right)$. If $B_o=4\times10^{-3}$ T and current $I=100\sqrt2$ A, the torque experienced by the loop is ________ Wb.A. ($\pi=3.14$)

A 5 mg particle carrying a charge of $5\pi\times10^{-6}$ C is moving with velocity of $\left(3\hat i+2\hat k\right)\times10^{-2}$ m/s in a region having magnetic field $\vec B=0.1\,\hat k$ Wb/m². It moves a distance of $\alpha$ meter along $\hat k$ when it completes 5 revolutions. The value of $\alpha$ is ________.

A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as $\alpha\dfrac{Q}{2M}$. The value of $\alpha$ is _____.