Electromagnetism PYQ — Page 9

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 $\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$)

Match List - I with List - II. \(\begin{array}{l|l} \text { List - I } & \text { List - II } \\ \hline \text { (A) }\begin{array}{l} \text { Electric field inside (distance } r>0 \text { from center) } \\ \text { of a uniformly charged spherical shell with } \\ \text { surface charge density } \sigma \text {, and radius R. } \end{array} & \text { (I) } \begin{array}{l} \sigma / \epsilon_0 \end{array} \\ \text { (B) } \begin{array}{l} \text { Electric field at distance r>0 from a uniformly } \\ \text { charged infinite plane sheet with surface } \\ \text { charge density } \sigma . \end{array} & \text { (II) } \sigma / 2 \epsilon_0 \\ \text { (C) } \begin{array}{l} \text { Electric field outside (distance r>0 from center) } \\ \text { of a uniformly charged spherical shell with } \\ \text { surface charge density } \sigma \text {, and radius R. } \end{array} & \text { (III) } 0 \\ \text { (D) } \begin{array}{l} \text { Electric field between } 2 \text { oppositely charged } \\ \text { infinite plane parallel sheets with uniform } \\ \text { surface charge density } \sigma . \end{array} & \text { (IV) } \frac{\sigma R^2}{\epsilon_0 r^2} \end{array}\) Choose the correct answer from the options given below :

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

At steady state the charge on the capacitor, as shown in the circuit below, is $\qquad$ $\mu \mathrm{C}$. 

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 : 

An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If $E$ is the electric field and $\varepsilon_0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R). Assertion (A) : Magnetic monopoles do not exist. Reason (R) : Magnetic field lines are continuous and form closed loops. In the light of the above statements, choose the most appropriate answer from the options given below :

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. 

Current passing through a wire as function of time is given as $\mathrm{I}(\mathrm{t})=0.02 \mathrm{t}+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 s$ to $t=2 s$ 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 : 

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below :

A long straight wire of a circular cross-section with radius ' $a$ ' carries a steady current $I$. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

A dipole with two electric charges of $2 \mu \mathrm{C}$ magnitude each, with separation distance $0.5 \mu \mathrm{~m}$, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by $30^{\circ}$ from the axis, it tends to realign in the direction due to a torque. The value of torque is :

The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of the surface is ________ $\mathrm{cm}^2$.

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 : 

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times 10^{-10} \mathrm{C}$, and masses $19.2 \times 10^{-27} \mathrm{~kg}$ and $9 \times 10^{-27} \mathrm{~kg}$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{45}$, where the value of 10$P$ is $\qquad$ (Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ ) Assume that charge may not be an integral multiple of electrons.

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8} \mathrm{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \mathrm{~N}$. The distance between them is (Take $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}$ as $9 \times 10^9 \mathrm{in} \mathrm{SI}$ units)

 Space between the plates of a parallel plate capacitor of plate area $4 \mathrm{~cm}^2$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ________ pF. $\left(\right.$ Given $\left.\varepsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)$

A parallel plate capacitor has charge $5 \times 10^{-6} \mathrm{C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6} \mathrm{C}$ then the dielectric constant of the slab is ________.

A parallel plate capacitor was made with two rectangular plates, each with a length of $l=3 \mathrm{~cm}$ and breath of $\mathrm{b}=1 \mathrm{~cm}$. The distance between the plates is $3 \mu \mathrm{~m}$. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. $l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ B. $l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}$ C. $l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}$ D. $l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}$ E. $l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ Choose the correct answer from the options given below:

Identify the valid statements relevant to the given circuit at the instant when the key is closed.  A. There will be no current through resistor $R$. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:

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 _____.

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.