The maximum magnetic field produced by a current of 12 A passing through a copper wire of diameter 1.2 mm is

Two moving coil galvanometers $A$ and $B$ having identical springs are placed in magnetic fields of 0.25 T and 0.5 T respectively. If the number of turns in $A$ and $B$ are respectively 36 and 48 and the areas of the coils $A$ and $B$ are $2.4 \times 10^{-3} \mathrm{~m}^2$ and $4.8 \times 10^{-3} \mathrm{~m}^2$ respectively, then the ratio of the current sensitivities of the galvanometer $A$ and $B$ is

If a wire of length ' $L$ ' carrying a current ' $i$ ' is bent in the shape of a semi-circular arc as shown in the figure, then the magnetic field at centre of the arc is

A galvanometer having 30 divisions has a current sensitivity of $0.0625 \frac{d i \nu}{\mu A}$. If it is converted into a voltmeter to read a maximum of 6 V , then the resistance of that voltmeter is

The magnetic field at the centre of a long solenoid having 400 turns per unit length and carrying a current ' $i$ ' is $6.24 \times 10^{-2} \mathrm{~T}$. The magnetic field at the centre of another long solenoid having 200 turns per unit length and carrying a current $\frac{i}{2}$ is

If a proton of kinetic energy 8.35 MeV enters a uniform magnetic field of 10 T at right angles to the direction of the field, then the force acting on the proton is

(Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and Charge of proton $=1.6 \times 10^{-19} \mathrm{C}$ )

Two charged particles of specific charges in the ratio 2:1 and masses in the ratio $1: 4$ moving with same kinetic energy enter a uniform magnetic field at right angles to the direction of the field. The ratio of the radii of the circular paths in which the particles move under the influence of the magnetic field is

A solenoid of one metre length and 3.55 cm inner diameter carries a current of 5 A . If the solenoid consists of five closely packed layers each with 700 turns along its length, then the magnetic field at its centre is

If a charged particle enters a uniform magnetic field normally with certain velocity, then the time period of revolution of the particle

A long straight wire of circular cross-section of radius ' $a$ ' is carrying a steady current. The current is distributed uniformly across the cross-section of the wire. The ratio of the magnetic fields at points $0.5 a$ and $1.5 a$ from the centre of the wire is

In a wire of radius 1 mm a steady current of 2 A uniformly distributed across the cross-section of the wire is flowing. Then the magnetic field at a point 0.25 mm from the centre of the wire is

The magnetic field at the centre of a current carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a point on its axis at a distance $R$ from its centre is $B_a$. The value of $\frac{B_c}{B_a}$ is

The force per unit length on a straight wire carrying current of 8 A making an angle of $30^{\circ}$ with a uniform magnetic field of 0.15 T is

An alpha particle moves along a circular path of radius 0.5 mm in a magnetic field of $2 \times 10^{-2} \mathrm{~T}$. The de-Broglie wavelength associated with the alpha particle is nearly (Planck's constant $=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ )

If a straight current carrying wire of linear density $0.12 \mathrm{~kg} \mathrm{~m}^{-1}$ is suspended in mid air by a uniform horizontal magnetic field of 0.5 T normal to the length of the wire, then the current through the wire is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$, Neglect Earth's magnetic field)

Two concentric loops $A$ and $B$ of same radius $2 \pi \mathrm{~cm}$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are 3 A and 4 A respectively, then the net magnetic field at their common centre is

The magnetic field at a distance of 10 cm from a long straight thin wire carrying a current of 4 A is

A velocity selector is to be constructed to select ions with a velocity of $6 \mathrm{~km} \mathrm{~s}^{-1}$. If the electric field used is $400 \mathrm{~V} \mathrm{~m}^{-1}$, then the magnetic field to be used is

A closely wound solenoid of 1200 turns and area of cross-section $5 \mathrm{~cm}^2$ carries a current. If the magnetic moment of the solenoid is $1.2 \mathrm{JT}^{-1}$, then the current through the solenoid is

Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. $I$ is current passing through each ring. The magnetic field value at the common centre is

An electron having kinetic energy of 100 eV circulates in a path of radius 10 cm in a magnetic field. The magnitude of magnetic field $|\mathbf{B}|$ is approximately [Mass of electron $=0.5 \mathrm{~MeV} \mathrm{c}^{-2}$, where c is the velocity of light].

A particle of mass $2.2 \times 10^{-30} \mathrm{~kg}$ and charge $1.6 \times 10^{-19} \mathrm{C}$ is moving at a speed of $10 \mathrm{~km} \mathrm{~s}^{-1}$ in a circular path of radius 2.8 cm inside a solenoid. The solenoid has $25 \frac{\text { turns }}{\mathrm{cm}}$ and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is

(Take, $\mu_0=4 \pi \times 10^{-7} \mathrm{~Hm}^{-1}$)

A toroid has a non ferromagnetic core of inner radius 24 cm and outer radius 25 cm , around which 4900 turns of a wire are wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is

Two infinitely long wires each carrying the same current and pointing in $+y$ direction are placed in the $x y$-plane, at $x=-2 \mathrm{~cm}$ and $x=1 \mathrm{~cm}$. An electron is fired with speed $u$ from the origin making an angle of $+45^{\circ}$ from the $X$-axis. The force on the electron at the instant it is fired is

[$B_0$ is the magnitude of the field at origin due to the wire at $x=1 \mathrm{~cm}$ alone].

Two electrons, $e_1$ and $e_2$ of mass $m$ and charge $q$ are injected into the perpendicular direction of the magnetic field $B$ such that the kinetic energy of $e_1$ is double than that of $e_2$. The relation of their frequencies of rotation, $f_1$ and $f_2$ is

Torque required to hold a small circular coil of 10 turns, area of $2 \times 10^{-4} \mathrm{~m}^2$ area of carrying 0.5 A current in the middle of a long solenoid of $10^3$ turns per metre carrying $3 \mathrm{~A}$ current, with its axis perpendicular to the axis of the solenoid is

Two concentric coils each of radius equal to $4 \pi ~\mathrm{cm}$ are placed at right angles to each other. If $10 \mathrm{~A}$ and $24 \mathrm{~A}$ are the currents flowing through the coils respectively, then the magnetic induction at the centre of the coils will be

A wire of length $L$ metre carrying a current $I$ ampere is bent in the form of a circle. Magnitude of its magnetic moment is

What is the net force on the square coil?

In a co-axial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero

The magnetic field, of a given length of wire for single turn coil, at its centre is B, then its value for two turns coil for the same wire is

In which of the following case no force exerted by a magnetic field on a charge?

A long thin hollow metallic cylinder of radius R has a current i ampere. The magnetic induction B away from the axis at a distance r from the axis varies as shown in