Magnetic Effects of Current

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then $X$ is nearly

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec E=E_0\hat j$ and $\vec B=B_0\hat j$. At time $t=0$, this charge has velocity $\vec v$ in the $x$-$y$ plane, making an angle $\theta$ with the $x$-axis. Which of the following option(s) is(are) correct for time $t>0$?

A cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\dfrac N{12}\mu_0aJ$, then the value of $N$ is

A circular wire loop of radius $R$ is placed in the $x$-$y$ plane centered at the origin $O$. A square loop of side $a$ $(a\ll R)$ having two turns is placed with its center at $z=\sqrt3R$ along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the $z$-axis. If the mutual inductance between the loops is given by $\dfrac{\mu_0a^2}{2^{p/2}R}$, then the value of $p$ is

A loop carrying current $I$ lies in the $x$-$y$ plane as shown in the figure. The unit vector $\hat k$ is coming out of the plane of the paper. The magnetic moment of the current loop is

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $|\vec B|$ as a function of the radial distance $r$ from the axis is best represented by

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A long circular tube of length 10 m and radius 0.3 m carries a current $I$ along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I=I_0\cos(300t)$ where $I_0$ is constant. If the magnetic moment of the loop is $N\mu_0I_0\sin(300t)$, then '$N$' is

A long insulated copper wire is closely wound as a spiral of '$N$' turns. The spiral has inner radius '$a$' and outer radius '$b$'. The spiral lies in the X-Y plane and a steady current '$I$' flows through the wire. The Z-component of the magnetic field at the center of the spiral is

Which of the field patterns given below is valid for electric field as well as for magnetic field?

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let $E$ be the electric field and $V$ be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let $B$ be the magnetic field at M and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

A steady current $I$ goes through a wire loop PQR having shape of a right angle triangle with PQ $=3x$, PR $=4x$ and QR $=5x$. If the magnitude of the magnetic field at P due to this loop is $k\left(\dfrac{\mu_0I}{48\pi x}\right)$, find the value of $k$.

A particle of mass $m$ and charge $q$, moving with velocity $V$ enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $\ell$. Choose the correct choice(s).

STATEMENT-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

and

STATEMENT-2: Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

A magnetic field $\vec B=B_0\hat j$ exists in the region $a<x<2a$ and $\vec B=-B_0\hat j$, in the region $2a<x<3a$, where $B_0$ is a positive constant. A positive point charge moving with a velocity $\vec v=v_0\hat i$, where $v_0$ is a positive constant, enters the magnetic field at $x=a$. The trajectory of the charge in this region can be like,

STATEMENT-1: A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.

because

STATEMENT-2: In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

Two wires each carrying a steady current $I$ are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.