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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 the semicircular portion of radius $R$ is lying in the Y-Z plane. The magnetic field at point $O$ is:
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 uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of: (i) an equilateral triangle of side $a$ (ii) a square of side $a$ The magnetic dipole moments of the coil in each case respectively are:
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 mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_0$ at a radius $R_0$. The mass is attached to a string that passes through a smooth hole in the plane, as shown in the figure. The tension in the string is increased gradually and finally, $m$ moves in a circle of radius $\frac{R_0}{2}$. The final value of the kinetic energy is:
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:
The angle between the electric lines of force and the equipotential surface is
Two identical long conducting wires $AOB$ and $COD$ are placed at right angle to each other, with one above other such that $O$ is their common point for the two. The wires carry $I_1$ and $I_2$ currents, 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:
When a uranium isotope $_{92}^{235}\mathrm{U}$ is bombarded with a neutron, it generates $_{36}^{89}\mathrm{Kr}$, three neutrons and:
An infinitely long straight conductor carries a current of $5 \text{ A}$. An electron is moving with a speed of $10^5 \text{ m/s}$ parallel to the conductor. The perpendicular distance between the electron and the conductor is $20 \text{ cm}$ at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is: (Take permeability of free space as $4\pi \times 10^{-7}$ SI units)
A circuit contains an ammeter, a battery of $30\text{ V}$ and a resistance $40.8\,\Omega$ all connected in series. If the ammeter has a coil of resistance $480\,\Omega$ and a shunt of $20\,\Omega$ then reading in the ammeter will be :
A disc of radius $2\text{ m}$ and mass $100\text{ kg}$ rolls on a horizontal floor. Its centre of mass has speed of $20\text{ cm/s}$. How much work is needed to stop it?
If the radius of the ${}_{13}^{27}\mathrm{Al}$ nucleus is taken to be $R_{\mathrm{Al}}$, then the radius of ${}_{53}^{125}\mathrm{Te}$ nucleus is nearly:
Consider the junction diode as ideal. The value of current flowing through AB is:
A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of $2$, the kinetic energy of the mass will:
A long solenoid of radius $1 \text{ mm}$ has $100$ turns per mm. If $1 \text{ A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
Which among the curves shown in the figure represents electrostatic field lines?
A uniform circular disc of radius $50 \text{ cm}$ at rest is free to turn about an axis that is perpendicular to its plane and passes through its centre. It is subjected to a torque that produces a constant angular acceleration of $2.0 \text{ rad/s}^2$. Its net acceleration in $\text{m/s}^2$ at the end of $2.0 \text{ s}$ is approximately:
Given below are two statements: Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current-carrying conductor only. 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.