Electromagnetic Induction

Figure shows a circular area of radius R where a uniform magnetic field $\vec B$ is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r) ?

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, 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 current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)

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

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

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments ab and cd. Then,

Two metallic rings A and B, identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings A and B jump to heights $h_A$ and $h_B$, respectively, with $h_A>h_B$. The possible relation(s) between their resistivities and their masses $m_A$ and $m_B$ is(are)

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II.

Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. 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.

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.