Magnetic Effects of Current

Two coaxial solenoids of different radii carry current I in the same direction. Let $\vec F_1$ be the magnetic force on the inner solenoid due to the outer one and $\vec F_2$ be the magnetic force on the outer solenoid due to the inner one. Then :

Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle 'θ' with the vertical. If wires have mass λ per unit length then the value of I is :

(g = gravitational acceleration)

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of 0.3 T in the positive $z$ direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?

A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd'. If 'α' be the angle of deviation of proton from initial direction of motion (see figure), the value of sin α will be :

A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization $\vec M$ (magnetic moment/volume), then $|\vec M|$ is :

If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n$^{\text{th}}$ level will be :

Two long straight parallel wires, carrying (adjustable) currents $I_1$ and $I_2$, are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product $I_1I_2$, would be :

A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle $2\theta_0$ at the centre of the circle (of which it forms an arch) then the tension in the wire is :

Two parallel wires in the plane of the paper are distance $X_0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\dfrac{X_0}{X_1}=3$, the value of $\dfrac{R_1}{R_2}$ is

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 Ω resistance, it can be converted into a voltmeter of range 0-30 V. If connected to a $\dfrac{2n}{249}\ \Omega$ resistance, it becomes an ammeter of range 0-1.5 A. The value of $n$ is

When $d\approx a$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case

Consider $d\gg a$, and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

A conductor lies along the z-axis at $-1.5\le z<1.5$ m and carries a fixed current of 10.0 A in $-\hat a_z$ direction (see figure). For a field $\vec B=3.0\times10^{-4}\,e^{-0.2x}\,\hat a_y$ T, find the power required to move the conductor at constant speed to $x=2.0$ m, $y=0$ m in $5\times10^{-3}$ s. Assume parallel motion along the $x$-axis.

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3\times10^3$ A m$^{-1}$. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is :

The radiation corresponding to $3\to2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times10^{-4}$ T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is :

A positive charge 'q' of mass 'm' is moving along the $+x$ axis. We wish to apply a uniform magnetic field B for time Δt so that the charge reverses its direction crossing the $y$ axis at a distance d. Then :

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1$, at its centre when a current I passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field $B_2$ at the centre of the loops when current I/3 passes through it. The ratio $B_1:B_2$ is :

A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 ms$^{-1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at $x=10$ cm from the wire is :

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $\vec u_1=4\hat i\ \mathrm{m\,s^{-1}}$, enters a region of uniform static magnetic field normal to the $x$-$y$ plane. The region of the magnetic field extends from $x=0$ to $x=L$ for all values of $y$. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity $\vec u_2=2\left(\sqrt3\hat i+\hat j\right)\ \mathrm{m\,s^{-1}}$. The correct statement(s) is (are)