Electromagnetism PYQ — Page 12

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

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.

The electric field of an electromagnetic wave in free space is $\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C$. The associated magnetic field in Tesla is

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)$ is :

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

In the given electromagnetic wave $\mathrm{E}_{\mathrm{y}}=600 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{Vm}^{-1}$, intensity of the associated light beam is (in $\mathrm{W} / \mathrm{m}^2$ : (Given $\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$$(L={l}^{2})$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times {10}^{-7}H$, where $x=$______.

Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} / \mathrm{m}^2$ is placed on $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}: 1$. The value of $n$ is_______.

Two coils have mutual inductance $0.002H$. The current changes in the first coil according to the relation $i={i}_{0}sin\omega t$, where ${i}_{0}=5A$ and $\omega =50\pi$ $\mathrm{rad}{s}^{-1}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi }{\alpha }V$. The value of $\alpha$ is

A parallel plate capacitor of capacitance $12.5 \mathrm{pF}$ is charged by a battery connected between its plates to potential difference of $12.0 \mathrm{~V}$. The battery is now disconnected and a dielectric slab $\left(\epsilon_{\mathrm{r}}=6\right)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ $10^{-12} \mathrm{~J}$.

In the following circuit, the battery has an emf of $2V$ and an internal resistance of $\frac{2}{3}\Omega$. The power consumption in the entire circuit is ______ $W$. 

A rectangular loop of sides $12\mathrm{cm}$ and $5\mathrm{cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively moves with a velocity of $5\mathrm{cm}{s}^{-1}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of ${10}^{-3}T{\mathrm{cm}}^{-1}$ along the negative $x$ direction and it is decreasing with time at the rate of ${10}^{-3}T{s}^{-1}.$ If the resistance of the loop is $6m\Omega$, the power dissipated by the loop as heat is ______ $\times {10}^{-9}W.$

If the net electric field at point $\mathrm{P}$ along $\mathrm{Y}$ axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$, where $x=$ _____. 

An electric field $\vec{E}=(2 x \hat{i}) N C^{-1}$ exists in space. A cube of side $2 \mathrm{~m}$ is placed in the space as per figure given below. The electric flux through the cube is ______ $\mathrm{Nm}^2 / \mathrm{C}$. 

A series $LR$ circuit connected with an ac source $E=(25\mathrm{sin}1000t)V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E=(20\mathrm{sin}2000t)V$, the new power factor of the circuit will be :

If frequency of electromagnetic wave is $60\mathrm{MHz}$ and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave $(\mathrm{in}m)$ is :

In the given figure $\mathrm{R}_1=10 \Omega, \mathrm{R}_2=8 \Omega, \mathrm{R}_3=4 \Omega$ and $\mathrm{R}_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively : 

A alternating current at any instant is given by $i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$ A. The $r m s$ value of the current is ________ A.

A coil is placed perpendicular to a magnetic field of $5000T$. When the field is changed to $3000T$ in $2s$, an induced emf of $22V$ is produced in the coil. If the diameter of the coil is $0.02m$, then the number of turns in the coil is:

A square loop of edge length $2 \mathrm{~m}$ carrying current of $2 \mathrm{~A}$ is placed with its edges parallel to the $x$ $y$ axis. A magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4 x) \hat{k}$, where $B_0=5 \mathrm{~T}$. The net magnetic force experienced by the loop is _______ $\mathrm{N}$.