Electromagnetism PYQ — Page 7

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)

Uniform magnetic fields of different strengths $\left(B_1\right.$ and $B_2$), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q , at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?  (Consider the velocity of the particle to be normal to the magnetic field and $B_2 \gt B_1$)

Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu \mathrm{C} / \mathrm{m}^2$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$)

Two point charges $-4 \mu c$ and $4 \mu c$, constituting an electric dipole, are placed at $(-9,0,0) \mathrm{cm}$ and $(9,0,0) \mathrm{cm}$ in a uniform electric field of strength $10^4 \mathrm{NC}^{-1}$. The work done on the dipole in rotating it from the equilibrium through $180^{\circ}$ is :

Two plane polarized light waves combine at a certain point whose electric field components are $\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}$ Find the amplitude of the resultant wave.

Two metal spheres of radius $R$ and $3 R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is.

Two long parallel wires $X$ and $Y$, separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $x \times 10^{-5} \mathrm{~T}$. The value of $x$ is__________ . Take permeability of free space as $\mu_0=4 \pi \times 10^{-7} \mathrm{SI}$ units. 

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is $V$. The potential difference between the points A and B (shown in the figure) is : 

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D points is : 

Two charges $\mathrm{q}_1$ and $\mathrm{q}_2$ are separated by a distance of 30 cm. A third charge $q_3$ initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from $C$ to $D$ is given by $\frac{\mathrm{q}_3 \mathrm{~K}}{4 \pi \epsilon_0}$, the value of K is : 

Two charges $7 \mu \mathrm{c}$ and $-4 \mu \mathrm{c}$ are placed at $(-7 \mathrm{~cm}, 0,0)$ and $(7 \mathrm{~cm}, 0,0)$ respectively. Given, $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$, the electrostatic potential energy of the charge configuration is :

Two cells of emf 1 V and 2 V and internal resistance $2 \Omega$ and $1 \Omega$, respectively, are connected in series with an external resistance of $6 \Omega$. The total current in the circuit is $\mathrm{I}_1$. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is _____.

Two capacitors $C_1$ and $C_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true? 

Three parallel plate capacitors $\mathrm{C}_1, \mathrm{C}_2$ and $\mathrm{C}_3$ each of capacitance $5 \mu \mathrm{~F}$ are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of $C_1$ capacitor is filled with a dielectric medium having dielectric constant of 4, is : 

Three infinitely long wires with linear charge density $\lambda$ are placed along the $x-a x i s, y$-axis and $z-$ axis respectively. Which of the following denotes an equipotential surface?

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 :

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A. 

The unit of $\sqrt{\frac{2 \mathrm{I}}{\epsilon_0 c}}$ is : (I = intensity of an electromagnetic wave, $\mathrm{c}:$ speed of light)

The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is given by : ($\mu_0$ is the permeability of free space and $\mu_{\mathrm{r}}$ is relative permeability)

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 :

The net current flowing in the given circuit is_______ A. 

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 :

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4} \mathrm{Tesla}$. If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ $\pi \mathrm{cm}$.

The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10 \mathrm{~cm}$ is 120 V. The potential at the centre of shell, at a distance $\mathrm{r}=5 \mathrm{~cm}$ from centre, and at a distance $\mathrm{r}=15 \mathrm{~cm}$ from the centre of the shell respectively, are :