Two identical long conducting wires $AOB$ and $COD$ are placed at right angles to each other, with one above the other such that $O$ is their common point. The wires carry currents $I_1$ and $I_2$ respectively. Point $P$ is lying at distance $d$ from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude

A wire carrying current $I$ has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to the x-axis while a semi-circular portion of radius $R$ is lying in a $yz$ plane. Magnetic field at point $O$ is

An npn-transistor is connected in common-emitter configuration in a given amplifier. A load resistance of 800 Ω is connected in the collector circuit and the voltage drop across it is 0.8 V. If the current amplification factor is 0.96 and the input resistance of the circuits is 192 Ω, the voltage gain and the power gain of the amplifier will, respectively, be

A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances (a/2) and (2a), respectively, from the axis of the wire is

A square loop ABCD carrying a current $i$ is placed near and coplanar with a long straight conductor XY carrying a current $I,$ the net force on the loop will be

A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3}$ Wb. The self-inductance of the solenoid is

A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $\mu A$ and is subjected to a magnetic field of strength 0.85 T. The work done for rotating the coil by $180°$against the torque is

In a common-emitter transistor amplifier, the audio signal voltage across the collector is 3 V. The resistance of collector is $3 k\Omega.$ If current gain is 100 and the base resistance is $2 k\Omega,$ the voltage and power gain of the amplifier is

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current I along the same direction is shown in the figure. Magnitude of force per unit length on the middle wire B is given by:

A long solenoid of diameter 0.1 m has $2 \times 10^4$ turns per meter. At the center of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is $10 \pi^2 \Omega,$ the total charge flowing through the coil during this time is

A metallic rod of mass per unit length $0.5$ kg/m is lying horizontally on a smooth inclined plane which makes an angle of $30^{\circ}$ with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction $0.25$ T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

Ionized hydrogen atoms and $\alpha$-particles with same momenta enter perpendicular to a constant magnetic field, $B$. The ratio of their radii of their paths $r_H : r_\alpha$ will be:

A cylindrical conductor of radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$ with the distance $d$ from the center of the conductor, is correctly represented by the figure:

A long solenoid of $50$ cm length having $100$ turns carries a current of $2.5$ A. The magnetic field at the centre of the solenoid is:$\newline (\mu_0 = 4\pi \times 10^{-7}$ T m A$^{-1})$

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of $10^5$ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is $20$ cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

A thick current carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B(r)$ due to the cable with the distance $r$ from the axis of the cable is represented by:

In the product $\vec{F} = q (\vec{v} \times \vec{B}) = q \vec{v} \times \left( \mathbf{B} \hat{i} + \mathbf{B} \hat{j} + \mathbf{B_0} \hat{k} \right),$ given $q = 1$ and $\vec{v} = 2\hat{i} + 4\hat{j} + 6\hat{k}, \newline$and force $\vec{F} = 4\hat{i} - 20\hat{j} + 12\hat{k},$ what will be the complete expression for $\vec{B}?$

A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of,$\newline (i)$ an equilateral triangle of side $a. \newline (ii)$ a square of side $a. \newline$The magnetic dipole moments of the coil in each case respectively are:

A screw gauge gives the following readings when used to measure the diameter of a wire.$\newline$Main scale reading: 0 mm$\newline$Circular scale reading: 52 divisions$\newline$Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

A long solenoid of radius $1$ mm has $100$ turns per mm. If $1$ A current flows in the solenoid, the magnetic field strength at the center of the solenoid is:

A square loop of side $1$ m and resistance $1 \Omega$ is placed in a magnetic field of $0.5$ T. If the plane of the loop is perpendicular to the direction of the magnetic field, the magnetic flux through the loop is:

Given below are two statements regarding Biot-Savart's law:$\newline$Statement I: Biot-Savart's law gives an expression for the magnetic field strength of an infinitesimal current element $(Idl)$ of a current carrying conductor only.$\newline$Statement II: Biot-Savart’s law is analogous to Coulomb's inverse square law of charge $q,$ with the former being related to the field produced by a scalar source, $Idl$ while the latter being produced by a vector source, $q. \newline$Choose the most appropriate answer:

From Ampere’s circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is:

A very long conducting wire is bent in a semi-circular shape from A to B as shown in the figure. The magnetic field at point P for steady current configuration is given by:

A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 4\hat{k})$ T. The magnitude of the magnetic force acting on the wire is: