Electromagnetism PYQ

A model for quantized motion of an electron in a uniform magnetic field $B$ states that the flux passing through the orbit of the electron is $n(h / e)$ where $n$ is an integer, $h$ is Planck's constant and $e$ is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( $m$ is the mass of the electron)

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :

Two identical charged conducting spheres $A$ and $B$ have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is $F$. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres $A$ and $B$ (Radii of $A$ and $B$ are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as :

The electric potential at distance r from a point charge q is V = q/(4πε₀r). The electric field E is:

The current passing through the battery in the given circuit, is : 

AB is a part of an electrical circuit (see figure). The potential difference " $\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}$ ", at the instant when current $\mathrm{i}=2 \mathrm{~A}$ and is increasing at a rate of $1 \mathrm{amp} / \mathrm{second}$ is : 

The electric field in a plane electromagnetic wave is given by $E_z=60 \cos \left(5 \mathrm{x}+1.5 \times 10^9 \mathrm{t}\right) \mathrm{V} / \mathrm{m} .$ Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

An electron (mass $9 \times 10^{-31} \mathrm{~kg}$ and charge $1.6 \times 10^{-19} \mathrm{C}$ ) moving with speed $\mathrm{c} / 100(\mathrm{c}=$ speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9 \times 10^{-4} \mathrm{~T}$ perpendicular to its direction of motion. We wish to apply an uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light $\mathrm{c}=3 \times 10^8 \mathrm{~ms}^{-1}$ )

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant $K_1$ and $K_2$ with thickness $\frac{3}{8} d$ and $\frac{d}{2}$, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. (If $K_1=1.25 K_2$, the value of $K_1$ is:

An electric dipole with dipole moment $5 \times 10^{-6} \mathrm{Cm}$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5 \mathrm{~N} / \mathrm{C}$ The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is:

A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is :- 

A 2 amp current is flowing through two different small circular copper coils having radii ratio $1: 2$. The ratio of their respective magnetic moments will be

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is :

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: A. hold the sheet there if it is magnetic. B. hold the sheet there if it is non-magnetic. C. move the sheet away from the pole with uniform velocity if it is conducting. D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar. Choose the correct statement(s) from the options given below:

The magnetic potential energy, when a magnetic bar of magnetic moment $\vec{m}$ is placed perpendicular to the magnetic field $\vec{B}$ is

The property which is not of an electromagnetic wave travelling in free space is that:

A uniform metal wire of length / has $10 \Omega$ resistance. Now this wire is stretched to a length $2 /$ and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is

The incorrect relation for a diamagnetic material (all the symbols carry their usual meaning and $\varepsilon$ is a small positive number) is

The amplitude of the charge oscillating in a circuit decreases exponentially as $Q=Q_0 e^{-R t 2 L}$, where $Q_0$ is the charge at $t=0 \mathrm{~s}$. The time at which charge amplitude decreases to $0.50 Q_0$ is nearly: [Given that $R=1.5 \Omega, L=12 \mathrm{mH}, \ln (2)=0.693$ ]

The steady state current in| the circuit shown below is : 

In a uniform magnetic field of 0.049 T , a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^2$. If the magnitude of magnetic moment of the needle is $x \times 10^{-5} \mathrm{Am}^2$, then the value of ' $x$ ' is : 

The given circuit shows a uniform straight wire $A B$ of 40 cm length fixed at both ends. In order to get zero reading in the galvanometer $G$, the free end of $J$ is to be placed from $B$ at: