Magnetic Effects of Current

As shown in the figure, a metallic rod of linear density 0.45 kg m$^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 T magnetic field is acting on it in the vertical upward direction, will be :

{Use g = 10 m/s$^2$}

A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be ______.

A triangular shaped wire carrying 10 A current is placed in a uniform magnetic field of 0.5 T, as shown in figure. The magnetic force on segment CD is

(Given BC = CD = BD = 5 cm.)

The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt3$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1/B_2$ will be

A closely wounded circular coil of radius 5 cm produces a magnetic field of $37.68\times10^{-4}$ T at its center. The current through the coil is _______ A.

[Given, number of turns in the coil is 100 and π = 3.14]

A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is _______ A-m$^2$. [Given π = 3.14]

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is

A wire of length 8 m is bent to form a circular loop in y-z plane. A current of 0.5 A is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is:

In the following loop, magnitude of the magnetic field produced at the centre (O) of the loop is : (Assume AB and CD are infinitely extended):

A long straight wire carries a current, $I = 2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time $t = 0$, the rod starts moving on the rails with a speed $v = 3.0$ m/s (see the figure).

A resistor $R = 1.4\ \Omega$ and a capacitor $C_o = 5.0\ \mu$F are connected in series between the rails. At time $t = 0$, $C_o$ is uncharged. Which of the following statement(s) is(are) correct? [$\mu_0 = 4\pi \times 10^{-7}$ SI units. Take $\ln 2 = 0.7$]

An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_\alpha$ and $r_S$, respectively. The ratio $(r_S/r_\alpha)$ is ____.

Two concentric circular loops, one of radius $R$ and the other of radius $2R$, lie in the $xy$-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction, with $I_2 > 2I_1$. $\vec B(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $xy$-plane. Which of the following statement(s) is(are) correct?

When the dipole $m$ is placed at a distance $r$ from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

A circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge $Q$ through a switch. The coil is in a horizontal uniform magnetic field $B_o$ parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

A conducting wire of parabolic shape, initially $y = x^2$, is moving with velocity $\vec V = V_0\hat i$ in a non-uniform magnetic field $\vec B = B_0\left(1 + \left(\frac yL\right)^\beta\right)\hat k$, as shown in figure. If $V_0$, $B_0$, $L$ and $\beta$ are positive constants and $\Delta\phi$ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000$ Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?

Two infinitely long straight wires lie in the $xy$-plane along the lines $x = \pm R$. The wire located at $x = +R$ carries a constant current $I_1$ and the wire located at $x = -R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0, 0, \sqrt3R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat j$ direction. Which of the following statements regarding the magnetic field $\vec B$ is (are) true?

In the $xy$-plane, the region $y > 0$ has a uniform magnetic field $B_1\hat k$ and the region $y < 0$ has another uniform magnetic field $B_2\hat k$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v_0 = \pi\ \mathrm{m\,s^{-1}}$ at $t = 0$, as shown in the figure. Neglect gravity in this problem. Let $t = T$ be the time when the particle crosses the $x$-axis from below for the first time. If $B_2 = 4B_1$, the average speed of the particle, in $\mathrm{m\,s^{-1}}$, along the $x$-axis in the time interval $T$ is ______.

A particle, of mass $10^{-3}$ kg and charge 1.0 C, is initially at rest. At time $t = 0$, the particle comes under the influence of an electric field $\vec{E}(t) = E_0 \sin\omega t\, \hat{i}$, where $E_0 = 1.0\ \mathrm{N\,C^{-1}}$ and $\omega = 10^3\ \mathrm{rad\,s^{-1}}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $\mathrm{m\,s^{-1}}$, attained by the particle at subsequent times is ____________.

A moving coil galvanometer has 50 turns and each turn has an area $2 \times 10^{-4}\ \mathrm{m^2}$. The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is $10^{-4}\ \mathrm{N\,m\,rad^{-1}}$. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 Ω. This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 − 1.0 A. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is __________.