Magnetic Effects of Current

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

A singly ionized magnesium atom (A=24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ______ cm.

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of $x$ A in the same direction. If the force of attraction per meter of each wire is $2\times10^{-6}$ N, then the value of $x$ is approximately :

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $\mu$T. The equal current flowing in the two conductors is :

Given below are two statements :

Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.

Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below :

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii $r_1$ and $r_2$ respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :

(Take : $e=1.6\times10^{-19}$ C, $m_p=1.67\times10^{-27}$ kg)

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5 and their respective masses ratio is 9 : 4. Then, the ratio of their charges will be :

A small square loop of wire of side $l$ is placed inside a large square loop of wire L ($L\gg l$). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

The electric current in a circular coil of 2 turns produces a magnetic induction $B_1$ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction $B_2$ at its centre. The ratio of $\dfrac{B_2}{B_1}$ is

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of $1\times10^{-4}$ Wbm$^{-2}$. The frequency of revolution of the electron will be (Take mass of electron $=9.0\times10^{-31}$ kg)

A charge particle is moving in a uniform magnetic field $\left(2\hat i+3\hat j\right)$ T. If it has an acceleration of $\left(\alpha\hat i-4\hat j\right)$ m/s$^2$, then the value of $\alpha$ will be :

$B_X$ and $B_Y$ are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of $B_X$ and $B_Y$ is :

Two concentric circular loops of radii $r_1$ = 30 cm and $r_2$ = 50 cm are placed in X-Y plane as shown in the figure. A current I = 7 A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

A velocity selector consists of electric field $\vec E=E\hat k$ and magnetic field $\vec B=B\hat j$ with B = 12 mT. The value of E required for an electron of energy 728 eV moving along the positive $x$-axis to pass undeflected is :

(Given, mass of electron = $9.1\times10^{-31}$ kg)

A beam of light travelling along X-axis is described by the electric field $E_y=900\sin\omega(t-x/c)$. The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of $3\times10^7$ ms$^{-1}$ will be :

(Given speed of light = $3\times10^8$ ms$^{-1}$)

An electron (mass m) with an initial velocity $\vec v=v_0\hat i$ $(v_0>0)$ is moving in an electric field $\vec E=-E_0\hat i$ $(E_0>0)$ where $E_0$ is constant. If at t = 0 de Broglie wavelength is $\lambda_0=\dfrac h{mv_0}$, then its de Broglie wavelength after time t is given by

A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of the cyclotron 'dees' is 60 cm, the kinetic energy of the accelerated protons in MeV will be :

[use $m_p=1.6\times10^{-27}$ kg, $e=1.6\times10^{-19}$ C]

The current sensitivity of a galvanometer can be increased by :

(A) decreasing the number of turns
(B) increasing the magnetic field
(C) decreasing the area of the coil
(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :