Question 1 :
Five identical capacitor plates, each of area {tex} \mathrm A {/tex}, are arranged such that adjacent plates are at a distance {tex} \mathrm d {/tex} apart, the plates are connected to a source of emf {tex} \mathrm V {/tex} as shown in the figure<br>The charge on plate 1 is {tex} \ldots \ldots {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d064f84aaed5b9dbb14ca">

Question 2 :
A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e19b57395419451d9946c32"><br>

Question 3 :
A charged shell of radius {tex} \mathrm { R } {/tex} carries a total charge {tex} \mathrm { Q } {/tex}. Given {tex} \phi {/tex} as the flux of electric field through a closed cylindrical surface of height {tex} h , {/tex} radius {tex} r {/tex} and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct?<br> [{tex} \varepsilon _ { 0 } \text {} {/tex} is the permittivity of free space ]<br>

Question 4 :
A disc of radius {tex} a / 4 {/tex} having a uniformly distributed charge {tex} 6 \mathrm { C } {/tex} is placed in the {tex} x - y {/tex} plane with its centre at {tex} ( - a / 2,0,0 ) {/tex} A rod of length {tex} a {/tex} carrying a uniformly distributed charge {tex} 8 \mathrm { C } {/tex} is placed on the {tex} x {/tex} -axis from {tex} x = a / 4 {/tex} to {tex} x = 5 a / 4 . {/tex} Two point charges {tex} - 7 \mathrm { C } {/tex} and {tex} 3 \mathrm { C } {/tex} are placed at {tex} ( a / 4 , - a / 4,0 ) {/tex} and {tex} ( - 3 a / 4,3 a / 4,0 ) , {/tex} respectively. Consider a cubical surface formed by six surfaces {tex} x = \pm a / 2 , y = \pm a / 2 , z = \pm a / 2 . {/tex} The electric flux through this cubical surface is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067c8d5af46bdd1fd8bb"><br>

Question 5 :
Two parallel plate capacitors of capacitances {tex} \mathrm C {/tex} and {tex} 2 \mathrm C {/tex} are connected in parallel and charged to a potential difference {tex} \mathrm V . {/tex} The battery is then disconnected and the region between the plates of the capacitor {tex}\mathrm C {/tex} is completely filled with a material of dielectric constant {tex} \mathrm K {/tex}. The potential differences across the capacitors now becomes...........

Question 6 :
Five point charges, each of value {tex} + q {/tex} coul, are placed on five vertices of a regular hexagon of side {tex} L {/tex} metres. The magnitude of the force on the point charge of value {tex} - q {/tex} coul. placed at the centre of the hexagen is {tex} \ldots \ldots \ldots \ldots \ldots . . {/tex} newton. <br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d0652baf4c75b8067941c"><br>

Question 7 :
Two identical capacitors, have the same capacitance {tex} C . {/tex} One of them is charged to potential {tex} V _ { 1 } {/tex} and the other {tex} V _ { 2 } . {/tex} The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

Question 8 :
A positively charged thin metal ring of radius {tex} R {/tex} is fixed in the {tex} x y {/tex} plane with its centre at the origin {tex} O . {/tex} A negatively charged particle {tex} P {/tex} is released from rest at the point {tex} \left( 0,0 , z _ { 0 } \right) {/tex} where {tex} z _ { 0 } > 0 . {/tex} Then the motion of {tex} P {/tex} is

Question 9 :
A hollow metal sphere of radius {tex} 5\ \mathrm { cms } {/tex} is charged such that the potential on its surface is 10 volts. The potential at the centre of the sphere is

Question 10 :
Eight mercury drops of equal radius and equal charge combine to form a big drop The capacitance of big drop in comparison the each small drop will be :

Question 11 :
A tiny spherical oil drop carrying a net charge {tex} \mathrm { q } {/tex} is balanced in still air with a vertical uniform electric field of strength {tex} \frac { 81 \pi } { 7 } \times 10 ^ { 5 } \mathrm { Vm } ^ { - 1 } {/tex}. When the field is switched off, the drop is observed to fall with terminal velocity {tex} 2 \times 10 ^ { - 3 } \mathrm { ms } ^ { - 1 } {/tex}. Given {tex} \mathrm { g } = 9.8 \mathrm { m } \mathrm { s } ^ { - 2 } {/tex}, viscosity of the air {tex} = 1.8 \times 10 ^ { - 5 } \mathrm { Ns } \mathrm { m } ^ { - 2 } {/tex} and the density of oil {tex} = 900 \mathrm { kg } \mathrm { m } ^ { - 3 } {/tex}, the magnitude of {tex} \mathrm { q } {/tex} is

Question 12 :
Four charges {tex} Q _ { 1 } , Q _ { 2 } , Q _ { 3 } {/tex} and {tex} Q _ { 4 } {/tex} of same magnitude are fixed along the {tex} x {/tex} axis at {tex} x = - 2 a , - a , + a {/tex} and {tex} + 2 a {/tex}, respectively. A positive charge {tex} q {/tex} is placed on the positive {tex} y {/tex} axis at a distance {tex} b > 0 {/tex}. Four options of the signs of these charges are given in List-I. The direction of the forces on the charge {tex} q {/tex} is given in List-II. Match List-I with List-II and select the correct answer using the code given below the lists.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d0da71781467f7340463a"><br><table><tr><th>List I</th> <th>List II </th> </tr><tr><td>P. {tex}Q_1,Q_2,Q_3,Q_4 {/tex} all positive</td> <td>1.{tex} +x{/tex}</td> </tr><tr><td>Q. {tex}Q_1, Q_2 {/tex} positive;{tex}Q_3,Q_4{/tex} negative </td> <td>2.{tex}-x{/tex}</td> </tr><tr><td>R. {tex}Q_1,Q_4 {/tex} positive;{tex}Q_2,Q_3{/tex} negative </td> <td>3.{tex}+y{/tex}</td> </tr><tr><td>S. {tex}Q_1, Q_3{/tex} positive;{tex}Q_2,Q_4{/tex} negative</td> <td>4.{tex}-y{/tex}</td> </tr></table>

Question 13 :
Two point charges {tex} + q {/tex} and {tex} - q {/tex} are held fixed at {tex} ( - d , o ) {/tex} and {tex} ( d , o ) {/tex} respectively of a {tex} x - y {/tex} coordinate system. Then

Question 14 :
Three concentric metallic spherical shells of radii {tex} R , 2 R , 3 R {/tex}, are given charges {tex} Q _ { 1 } , Q _ { 2 } , Q _ { 3 } , {/tex} respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, {tex} Q _ { 1 }: Q _ { 2 }: Q _ { 3 } , {/tex} is

Question 15 :
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067984aaed5b9dbb14fe"><br>

Question 16 :
A wooden block performs SHM on a frictionless surface with frequency, {tex} v _ { 0 } {/tex}. The block carries a charge {tex} + Q {/tex} on its surface. If now a uniform electric field {tex} \vec { E } {/tex} is switched-on as shown, then the SHM of the block will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d06808d5af46bdd1fd8c6"><br>

Question 17 :
Six charges of equal magnitude, 3 positive and 3 negative are to be placed on {tex} P Q R S T U {/tex} corners of a regular hexagon, such that field at the centre is double that of what it would have been if only one + ve charge is placed at {tex} R {/tex}. Which of the following arrangement of charge is possible for {tex} P , Q , R ,S, T {/tex} and {tex}U {/tex} respectively.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067784aaed5b9dbb14f5"><br>

Question 18 :
A {tex} 2 \mu F {/tex} capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067f8d5af46bdd1fd8c1">''<br>

Question 19 :
Three infinitely long charge sheets are placed as shown in figure. The electric field at point {tex} \mathrm P {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067884aaed5b9dbb14fa"><br>

Question 20 :
In the given circuit, a charge of {tex} + 80 \mu C {/tex} is given to the upper plate of the {tex} 4 \mu F {/tex} capacitor. Then in the steady state, the charge on the upper plate of the {tex} 3 \mu F {/tex} capacitor is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d0682fba05a6bf9521e2f"><br>

Question 21 :
Consider a system of three charges {tex} q / 3 , q / 3 {/tex} and {tex} - 2 q / 3 {/tex} placed at points {tex} \mathrm {A , B }{/tex} and {tex} \mathrm C {/tex}, respectively, as shown in the figure. Take {tex}\mathrm O {/tex} to be the centre of the circle of radius {tex} \mathrm { R } {/tex} and angle {tex} \mathrm {C A B} = 60 ^ { \circ } {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067a84aaed5b9dbb1501"><br>

Question 22 :
A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d0678baf4c75b8067943e"><br>

Question 23 :
A parallel plate capacitor {tex} \mathrm C {/tex} with plates of unit area and separation dis filled with a liquid of dielectric constant {tex}\mathrm K = 2 . {/tex} The level of liquid is {tex} d / 3 {/tex} initially. Suppose the liquid level decreases at a constant speed {tex} v , {/tex} the time constant as a function of time {tex} t {/tex} is {tex} - {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d067b84aaed5b9dbb1503"><br>

Question 24 :
Charges {tex} Q , 2 Q {/tex} and {tex} 4 Q {/tex} are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii {tex} R / 2 , R {/tex} and {tex} 2 R {/tex} respectively, as shown in figure. If magnitude of the electric fields at point {tex} P {/tex} at a distance {tex} R {/tex} from the centre of sphere 1,2 and 3 are {tex} E _ { 1 } , E _ { 2 } {/tex} and {tex} E _ { 3 } {/tex} respectively, then <br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d06828d5af46bdd1fd8cd"><br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2d0683fba05a6bf9521e31">

Question 25 :
Two equal point charges are fixed at {tex} x = - a {/tex} and {tex} x = + a {/tex} on the {tex} x {/tex} -axis. Another point charge {tex} Q {/tex} is placed at the origin. The change in the electrical potential energy of {tex} Q {/tex}, when it is displaced by a small distance {tex} x {/tex} along the {tex} x {/tex} -axis, is approximately proportional to

Question 26 :
A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

Question 27 :
A cubical region of side {tex} a {/tex} has its centre at the origin. It encloses three fixed point charges, {tex} - q {/tex} at {tex} ( 0 , - a / 4,0 ) , + 3 q {/tex} at {tex} ( 0,0,0 ) {/tex} and {tex} - q {/tex} at {tex} ( 0 , + a / 4,0 ) . {/tex} Choose the correct options(s)<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e19b6c495419451d9946d45"><br>

Question 28 :
Two non-conducting spheres of radii {tex} \mathrm { R } _ { 1 } {/tex} and {tex} \mathrm { R } _ { 2 } {/tex} and carrying uniform volume charge densities {tex} + \rho {/tex} and {tex} - \rho , {/tex} respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e19b70c95419451d9946d65"><br>

Question 29 :
The magnitude of electric field {tex} \vec { E } {/tex} in the annular region of a charged cylindrical capacitor.

Question 30 :
Charges<em>Q</em>₁and<em>Q</em>₂lie inside and outside respectively of a closed Gaussian surface <em>S</em>. Let <em>E</em> be the field at any point on <em>S</em> and <em><font face="Symbol">&phi;</font></em> be the flux of <em>E</em> over <em>S</em>: