Electromagnetism PYQ — Page 10

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 :

A parallel plate capacitor of area $A=16 \mathrm{~cm}^2$ and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area $\mathrm{A}_0=3.2 \mathrm{~cm}^2$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $\mathrm{A}_0$ is ________ mA .

From the combination of resistors with resistance values $R_1=R_2=R_3=5 \Omega$ and $R_4=10 \Omega$, which of the following combination is the best circuit to get an equivalent resistance of $6 \Omega$ ?

A particle of charge $1.6 \mu \mathrm{C}$ and mass $16 \mu \mathrm{~g}$ is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ S. $(\pi=3.14)$

Consider a moving coil galvanomenter (MCG): A. The torsional constant in moving coil galvanometer has dimentions $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$ B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns $(\mathrm{N})$ to its double $(2 \mathrm{~N})$, then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is $\ldots\ldots$ -. [Take mass of electron $\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}$, charge of electron $\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}$, $\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]$

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathrm{R}$ Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason $\mathrm{R}$ : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below

A capacitor, $C_1=6 \mu \mathrm{~F}$ is charged to a potential difference of $\mathrm{V}_0=5 \mathrm{~V}$ using a 5 V battery. The battery is removed and another capacitor, $\mathrm{C}_2=12 \mu \mathrm{~F}$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges $\left(q_1\right.$ and $\left.q_2\right)$ on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached. 

A point charge +q is placed at the origin. A second point charge +9 q is placed at $(\mathrm{d}, 0,0)$ in Cartesian coordinate system. The point in between them where the electric field vanishes is :

For ac circuit shown in figure, $\mathrm{R}=100 \mathrm{k} \Omega$ and $\mathrm{C}=100 \mathrm{pF}$ and the phase difference between $\mathrm{V}_{\text {in }}$ and $\left(V_B-V_A\right)$ is $90^{\circ}$. The input signal frequency is $10^x \mathrm{rad} / \mathrm{sec}$, where ' x ' is ______ 

The magnetic field of an E.M. wave is given by $\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{z}{\mathrm{c}}\right)\right]$ (S.I. Units). The corresponding electric field in S.I. units is :

There are ' $n$ ' number of identical electric bulbs, each is designed to draw a power $p$ independently from the mains supply. They are now joined in series across the main supply. The total power drawn by the combination is :

A wire of resistance $9 \Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_{\mathrm{o}}$. Choose the correct option from the following. 

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 \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

Consider a circular loop that is uniformly charged and has a radius $\mathrm{a} \sqrt{2}$. Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

Electric charge is transferred to an irregular metallic disk as shown in figure. If $\sigma_1, \sigma_2, \sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below:  

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

 In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by :

Four capacitor each of capacitance $16 \mu \mathrm{~F}$ are connected as shown in the figure. The capacitance between points A and B is : ______ (in $\mu \mathrm{F}$). 

A small bob of mass 100 mg and charge $+10 \mu \mathrm{C}$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be : (Given, $\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}$ and acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$) 

A parallel-plate capacitor of capacitance $40 \mu \mathrm{~F}$ is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant $\mathrm{K}=2$. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

The battery of a mobile phone is rated as 4.2 V , 5800 mAh. How much energy is stored in it when fully charged ?

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN.