An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

A long straight wire of a circular cross-section with radius ' a ' carries a steady current I . The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge " $q$ " is released at a distance " $a$ " from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is [ ${\mu }_0$ is vacuum permeability]

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius $R$ carrying current I. Let ${\mathrm{B}}_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x:\mathrm{R}=3:4,\frac{{\mathrm{B}}_2}{{\mathrm{B}}_1}$ is :

A particle of charge $q$, mass $m$ and kinetic energy $E$ enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of $r$ with $E$ ?

Uniform magnetic fields of different strengths $(B_1$ and $B_2)$, both normal to the plane of the paper exist as shown in the figure. A charged particle of mass $m$ and charge $q$, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and ${\mathrm{B}}_2>{\mathrm{B}}_1$ )

In a moving coil galvanometer, two moving coils ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ have the following particulars : $$\begin{array}{rl}& {\mathrm{R}}_1=5\Omega ,{\mathrm{N}}_1=15,{\mathrm{A}}_1=3.6\times 10^{-3}{\mathrm{m}}^2,{\mathrm{B}}_1=0.25\mathrm{T}\\ & {\mathrm{R}}_2=7\Omega ,{\mathrm{N}}_2=21,{\mathrm{A}}_2=1.8\times 10^{-3}{\mathrm{m}}^2,{\mathrm{B}}_2=0.50\mathrm{T}\end{array}$$ Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

Given below are two statements: one is labelled as $\mathbf{Assertion}\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : If Oxygen ion $\left({\mathrm{O}}^{-2}\right)$ and Hydrogen ion $\left({\mathrm{H}}^{+}\right)$enter normal to the magnetic field with equal momentum, then the path of ${\mathrm{O}}^{-2}$ ion has a smaller curvature than that of ${\mathrm{H}}^{+}$. Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statements, choose the correct answer from the options given below

A balloon and its content having mass M is moving up with an acceleration ‘a’. The mass that must be released from the content so that the balloon starts moving up with an acceleration ‘3a’ will be(Take ‘g’ as acceleration due to gravity)

A body of mass 2 kg moving with velocity of ${\vec{v}}_{in}=3\hat{i}+4\hat{j}{\text{ ms}}^{-1}$ enters into a constant force field of 6N directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is.

A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ }$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively, are (in N ) : (Take acceleration due to gravity $10\mathrm{m}/{\mathrm{s}}^2$ )

An object with mass 500 g moves along x-axis with speed $v=4\sqrt{x}$ m/s. The force acting on the object is :

A body of mass $m$ is suspended by two strings making angles ${\theta }_1$ and ${\theta }_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3}{T}_2$, the angles ${\theta }_1$ and ${\theta }_2$ are

A block of mass 1 kg , moving along $x$ with speed $v_i=10\mathrm{m}/\mathrm{s}$ enters a rough region ranging from $x=0.1\mathrm{m}$ to $x=1.9\mathrm{m}$. The retarding force acting on the block in this range is ${\mathrm{F}}_{\mathrm{r}}=-\mathrm{kr}\mathrm{N}$, with k $=10\mathrm{N}/\mathrm{m}$. Then the final speed of the block as it crosses rough region is.

A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are :