Magnetic Effects of Current and Magnetism

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 ______ $\mu$T. ($\frac{\mu_0}{4\pi}=10^{-7}$ N/A$^2$)

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 $(4\hat i+2\hat j)\times10^{-10}$ N. The velocity of the particle at that instant is ______ m/s.

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.m$^2$. 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 $30^\circ$ 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 $(3\hat{i} + 2\hat{j})$ T has an acceleration $\left(4\hat{i} - \frac{x}{2}\hat{j}\right)\mathrm{m/s^2}$. The value of $x$ is

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec v=\left(\frac{v_0}{\sqrt2}\hat x+\frac{v_0}{\sqrt2}\hat y\right)$. 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 ________. ($\mu_0=4\pi\times10^{-7}$ Tm/A, $\pi=3.14$)

A current carrying circular loop of radius 2 cm with unit normal $\hat n=\frac{\hat k+\hat i}{\sqrt2}$ is placed in a magnetic field, $\vec B=B_0(3\hat i+2\hat k)$. If $B_0=4\times10^{-3}$ 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 $(3\hat i+2\hat k)\times10^{-2}$ m/s in a region having magnetic field $\vec B=0.1\,\hat k$ Wb/m$^2$. It moves a distance of $\alpha$ meter along $\hat k$ when it completes 5 revolutions. The value of $\alpha$ is ______.