Correct4
Incorrect-1
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
The electric field {tex} E {/tex} at all points on the {tex} x {/tex} -axis has the same direction
Electric field at all points on {tex} y {/tex} -axis is along {tex} x {/tex} -axis
Work has to be done in bringing a test charge from {tex}\infty {/tex} to the origin
The dipole moment is {tex} 2 q d {/tex} along the {tex} x {/tex} -axis
Correct4
Incorrect-1
A parallel plate capacitor of capacitance {tex} C {/tex} is connected to a battery and is charged to a potential difference {tex} V {/tex}. Another capacitor of capacitance {tex} 2 C {/tex} is similarly charged to a potential difference {tex} 2 V {/tex}. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
zero
{tex} \frac { 3 } { 2 } C V ^ { 2 } {/tex}
{tex} \frac { 25 } { 6 } C V ^ { 2 } {/tex}
{tex} \frac { 9 } { 2 } C V ^ { 2 } {/tex}
Correct4
Incorrect-1
Two identical metal plates are given positive charges {tex} Q _ { 1 } {/tex} and {tex} Q _ { 2 } \left( < Q _ { 1 } \right) {/tex} respectively. If they are now brought close together to form a parallel plate capacitor with capacitance {tex} C , {/tex} the potential difference between them is
{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / ( 2 C ) {/tex}
{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / C {/tex}
{tex} \left( Q _ { 1 } - Q _ { 2 } \right) / C {/tex}
{tex} \left( Q _ { 1 } - { Q } _ { 2 } \right) / ( 2 C ) {/tex}
Correct4
Incorrect-1
Three charges {tex} Q , + q {/tex} and {tex} + q {/tex} are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if {tex} Q {/tex} is equal to
{tex} \frac { - q } { 1 + \sqrt { 2 } } {/tex}
{tex} \frac { - 2 q } { 2 + \sqrt { 2 } } {/tex}
{tex} - 2 q {/tex}
{tex} + q {/tex}
Correct4
Incorrect-1
A parallel plate capacitor of area {tex} A , {/tex} plate separation {tex} d {/tex} and capacitance {tex} C {/tex} is filled with three different dielectric materials having dielectric constants {tex} k _ { 1 } , k _ { 2 } {/tex} and {tex} k _ { 3 } {/tex} as shown. If a single dielectric material is to be used to have the same capacitance {tex} C {/tex} in this capacitor, then its dielectric constant {tex} k {/tex} is given by
{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } } + \frac { 1 } { K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}
{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } + K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}
{tex} K = \frac { K _ { 1 } K _ { 2 } } { K _ { 1 } + K _ { 2 } } + 2 K _ { 3 } {/tex}
{tex} K = K _ { 1 } + K _ { 2 } + 2 K _ { 3 } {/tex}
Correct4
Incorrect-1
Three positive charges of equal value {tex} q {/tex} are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in
Correct4
Incorrect-1
Consider the situation shown in the figure. The capacitor {tex} A {/tex} has a charge {tex} q {/tex} on it whereas {tex} B {/tex} is uncharged. The charge appearing on the capacitor {tex} B {/tex} a long time after the switch is closed is
zero
{tex} q / 2 {/tex}
{tex} q {/tex}
{tex} 2 q {/tex}
Correct4
Incorrect-1
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
{tex} \frac { 1 } { 4 } C \left( V _ { 1 } ^ { 2 } - V _ { 2 } ^ { 2 } \right) {/tex}
{tex} \frac { 1 } { 4 } C \left( V _ { 1 } ^ { 2 } + V _ { 2 } ^ { 2 } \right) {/tex}
{tex} \frac { 1 } { 4 } C \left( V _ { 1 } - V _ { 2 } \right) ^ { 2 } {/tex}
{tex} \frac { 1 } { 4 } C \left( V _ { 1 } + V _ { 2 } \right) ^ { 2 } {/tex}
Correct4
Incorrect-1
A metallic shell has a point charge {tex} ^ { \prime } q ^ { \prime } {/tex} kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces?
Correct4
Incorrect-1
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.
{tex} + , + , + , - , - , - {/tex}
{tex} - , + , + , + , - , - {/tex}
{tex} - , + , + , - , + , - {/tex}
{tex} + , - , + , - , + , - {/tex}
Correct4
Incorrect-1
A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be
due to {tex} q _ { 1 } {/tex} and {tex} q _ { 2 } {/tex} only
due to {tex} q _ { 2 } {/tex} only
Zero
due to all
Correct4
Incorrect-1
Three infinitely long charge sheets are placed as shown in figure. The electric field at point {tex} P {/tex} is
{tex} \frac { 2 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}
{tex} \frac { 4 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}
{tex} - \frac { 2 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}
{tex} - \frac { 4 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}
Correct4
Incorrect-1
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
zero everywhere
non-zero and uniform
non-uniform
zero only at its center
Correct4
Incorrect-1
Consider a system of three charges {tex} q / 3 , q / 3 {/tex} and {tex} - 2 q / 3 {/tex} placed at points {tex} A , B {/tex} and {tex} C , {/tex} respectively, as shown in the figure. Take {tex} O {/tex} to be the centre of the circle of radius {tex} \mathrm { R } {/tex} and angle {tex} C A B = 60 ^ { \circ } {/tex}
The electric field at point {tex} O {/tex} is {tex} \frac { q } { 8 \pi \varepsilon _ { 0 } R ^ { 2 } } {/tex} directed along the negative {tex} x {/tex} -axis
The potential energy of the system is zero
The magnitude of the force between the charges at {tex} C {/tex} and {tex} B {/tex} is {tex} \frac { q ^ { 2 } } { 54 \pi \varepsilon _ { 0 } R ^ { 2 } } {/tex}
The potential at point {tex} O {/tex} is {tex} \frac { q } { 12 \pi \varepsilon _ { 0 } R } {/tex}
Correct4
Incorrect-1
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
1: 2: 3
1: 3: 5
1: 4: 9
1: 8: 18
Correct4
Incorrect-1
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
{tex} \frac { - 2 C } { \varepsilon _ { 0 } } {/tex}
{tex} \frac { 2 C } { \varepsilon _ { 0 } } {/tex}
{tex} \frac { 10 C } { \varepsilon _ { 0 } } {/tex}
{tex} \frac { 12 C } { \varepsilon _ { 0 } } {/tex}
Correct4
Incorrect-1
Consider an electric field {tex} \vec { E } = E _ { 0 } \hat { x } {/tex} where {tex} \mathrm { E } _ { 0 } {/tex} is a constant. The flux through the shaded area (as shown in the figure) due to this field is
{tex} 2 E _ { 0 } a _ { 2 } {/tex}
{tex} \sqrt { 2 } E _ { 0 } a ^ { 2 } {/tex}
{tex} E _ { 0 } \mathrm { a } ^ { 2 } {/tex}
{tex} \frac { E _ { 0 } a ^ { 2 } } { \sqrt { 2 } } {/tex}
Correct4
Incorrect-1
In the given arrangement of capacitors, {tex} 6 \mu \mathrm { C } {/tex} charge is added to point {tex} a {/tex}. Find the charge on upper capacitor
{tex} 3 \mu \mathrm { C } {/tex}
{tex} 1 \mu \mathrm { C } {/tex}
{tex} 2 \mu \mathrm {C} {/tex}
{tex} 6 \mu \mathrm { C } {/tex}
Correct4
Incorrect-1
Consider three concentric shells of metal {tex} A , B {/tex} and {tex} C {/tex} are having radii {tex} a , b {/tex} and {tex} c {/tex} respectively as shown in the figure {tex} ( a < b < c ) {/tex}. Their surface charge densities are {tex} \sigma , - \sigma {/tex} and {tex} \sigma {/tex} respectively. Calculate the electric potential on the surface of shell {tex} A {/tex}
{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a - b + c ) {/tex}
{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a - b - c ) {/tex}
{tex} \frac { \sigma } { \varepsilon _ { 0 } } \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } \right) {/tex}
{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a + b - c ) {/tex}
Correct4
Incorrect-1
Three capacitors of capacitance {tex} 1 \mu \mathrm { F } , 2 \mu \mathrm { F } {/tex} and {tex} 3 \mu \mathrm { F } {/tex} are connected in series and a potential difference of {tex} 11 \mathrm { V } {/tex} is applied across the combination. Then, the potential difference across the plate of {tex} 1 \mu \mathrm { F } {/tex} capacitor is
{tex} 2 \mathrm { V } {/tex}
{tex} 4 \mathrm { V } {/tex}
{tex} 1 \mathrm { V } {/tex}
{tex} 6 \mathrm { V } {/tex}
Correct4
Incorrect-1
An electric charge {tex} 10 ^ { - 3 }\mu \mathrm { C } {/tex} is placed at the origin {tex} ( 0,0 ) {/tex} of {tex} X -Y{/tex} coordinate system. Two points {tex} A {/tex} and {tex} B {/tex} are situated at {tex} ( \sqrt { 2 } , \sqrt { 2 } ) {/tex} and {tex} ( 2,0 ) {/tex} respectively. The potential difference between the points {tex} A {/tex} and {tex} B {/tex} will be
{tex} 9 \mathrm { V } {/tex}
Zero
{tex} 2 \mathrm { V } {/tex}
{tex} 4.5 \mathrm { V } {/tex}
Correct4
Incorrect-1
The potential to which a conductor is raised, depends on
The amount of charge
Geometry and size of the conductor
Both (a) and (b)
Only on (a)
Correct4
Incorrect-1
Three capacitors {tex} C _ { 1 } , C _ { 2 } {/tex} and {tex} C _ { 3 } {/tex} are connected as shown in the figure to a battery of {tex} V {/tex} volt. If the capacitor {tex} C _ { 3 } {/tex} breaks down electrically the change in total charge on the combination of capacitors is
{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 - \left( \frac { C _ { 3 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}
{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 - \left( \frac { \left( C _ { 1 } + C _ { 2 } \right) } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}
{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 + \left( \frac { C _ { 3 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}
{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 + \left( \frac { C _ { 2 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}
Correct4
Incorrect-1
Two charges {tex} + q {/tex} and {tex} - q {/tex} are kept apart. Then at any point on the right bisector of line joining the two charges
The electric field strength is zero
The electric potential is zero
Both electric potential and electric field strength are zero.
Both electric potential and electric field strength are non-zero.
Correct4
Incorrect-1
An electric field is expressed as {tex} \vec { E } = 2 \hat { \imath } + 3 \hat { j } {/tex}. Find the potential difference {tex} \left( V _ { A } - V _ { B } \right) {/tex} between two points {tex} A {/tex} and {tex} B {/tex} whose position vectors are given by {tex} r _ { A } = \hat { \imath } + 2 \hat { j } {/tex} and {tex} r _ { B } = 2 \hat { \imath } + \hat { \jmath } + 3 \hat { k } {/tex}
{tex} - 1 \mathrm { V } {/tex}
{tex} 1 \mathrm { V } {/tex}
{tex} 2 \mathrm { V } {/tex}
{tex} 3 \mathrm { V } {/tex}
