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Q 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}
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Q 2. 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}
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Q 3. 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
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Q 4. 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}
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Q 5. 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 dieletric material is to be used to have the same capacitance {tex} C {/tex} is this capacitors, 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}
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Q 6. In the arrangement of capacitors shown in figure, each capacitor is of {tex} 9 \mu F , {/tex} Then the equivalent capacitance between in points {tex} A {/tex} and {tex} B {/tex} is
{tex} 9 \mu \mathrm F {/tex}
{tex} 18 \mu \mathrm F {/tex}
{tex} 4.5 \mu \mathrm F {/tex}
{tex} 15\mu \mathrm F {/tex}
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Q 7. Three identical metallic uncharged spheres {tex} A , B {/tex} and {tex} C {/tex} each of radius {tex} a {/tex}, are kept at the corners of an equilateral triangle of side {tex} d ( d \gg a ) {/tex} as shown in Fig. The fourth sphere (of radius {tex} a {/tex} ), which has a charge {tex} q {/tex}, touches {tex} A {/tex} and is then removed to a position far away. {tex} B {/tex} is earthed and then the earth connection is removed. {tex}C {/tex} is then earthed. The charge on {tex} C {/tex} is
{tex} \frac { q a } { 2 d } \left( \frac { 2 d - a } { 2 d } \right) {/tex}
{tex} \frac { q a } { 2 d } \left( \frac { 2 d - a } { d } \right) {/tex}
{tex} - \frac { q a } { 2 d } \left( \frac { d - a } { d } \right) {/tex}
{tex} \frac { 2 q a } { d } \left( \frac { d - a } { 2 d } \right) {/tex}
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Q 8. Two copper spheres of same radii, one hollow and the other solid, are charged to same potential. Then, which, if any, of the two will have more charge?
Hollow
Solid
Both will have the same charge
Nothing can be predicted
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Q 9. In the electric field of a point charge {tex} q {/tex}, a certain point charges is carried from point {tex} A {/tex} to {tex} B , C , D {/tex} and {tex} E {/tex} as shown in figue The work done is
Least along the path {tex} A E {/tex}
Least along the path {tex} A C {/tex}
Zero along any one of the paths
Least along {tex} A B {/tex}
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Q 10. Each capacitor shown in figure is {tex} 2 \mu \mathrm { F } . {/tex} Then the equivalent capacitance between points {tex} A {/tex} and {tex} B {/tex} is
{tex} 2 \mu \mathrm { F } {/tex}
{tex} 4\mu \mathrm F {/tex}
{tex} 6 \mu \mathrm F {/tex}
{tex} 8 \mu \mathrm { F } {/tex}
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Q 11. Some equipotential surfaces are shown in Fig. The magnitude and direction of the electric field is
{tex} 100 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 120 ^ { \circ } {/tex} with the {tex} x {/tex} -axis
{tex} 200 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 60 ^ { \circ } {/tex} with the {tex} x {/tex} -axis
{tex} 200 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 120 ^ { \circ } {/tex} with the {tex} x {/tex} -axis
None of the above
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Q 12. Charges {tex} 2 q , - q {/tex} and {tex} - q {/tex} lie at the vertices of a triangle. The value of {tex} E {/tex} and {tex} V {/tex} at the centroid of equilateral triangle will be
{tex} \mathrm { E } \neq 0 {/tex} and {tex} \mathrm { V } \neq 0 {/tex}
{tex} \mathrm { E } = 0 {/tex} and {tex} \mathrm { V } = 0 {/tex}
{tex} \mathrm { E } \neq 0 {/tex} and {tex} \mathrm { V } = 0 {/tex}
{tex} \mathrm { E } = 0 {/tex} and {tex} \mathrm { V } \neq 0 {/tex}
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Q 13. For the circuit shown in figure the charge on {tex} 4 \mu \mathrm { F } {/tex} capacitor is
{tex} 40 \mu C {/tex}
{tex} 30 \mu C {/tex}
{tex} 24 \mu C {/tex}
{tex} 54 \mu C {/tex}
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Q 14. Three infinite planes have a uniform surface charge distribution {tex} \sigma {/tex} on its surface. All charges are fixed. On each of the three infinite planes, parallel to the {tex} y - z {/tex} plane placed at {tex} x = - a , x = 0 {/tex} and {tex} x = a {/tex}. There is a uniform surface charge of the same density, {tex} \sigma {/tex}
The potential difference between {tex} A {/tex} and {tex} C {/tex} is
{tex} \frac { \sigma } { 2 \varepsilon _ { 0 } } a {/tex}
{tex} \frac { \sigma } { \varepsilon _ { 0 } } a {/tex}
{tex} \frac { \sigma a } { 2 \varepsilon _ { 0 } } {/tex}
None of the above
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Q 15. Five balls numbered {tex} 1,2,3,4,5 {/tex} are suspended using separate threads. The balls {tex} ( 1,2 ) , ( 2,4 ) {/tex} and {tex} ( 4,1 ) {/tex} show electrostatic attraction, while balls {tex} ( 2,3 ) {/tex} and {tex} ( 4,5 ) {/tex} show repulsion. Therefore, ball {tex}1{/tex} must be
Negatively charged
Positively charged
Neutral
Made of metal
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Q 16. A dielectric in the form of a sphere is introduced into a homogeneous electric field. {tex} A , B {/tex} and {tex} C {/tex} are three points as shown in fig
Then,
Intensity at {tex} A {/tex} increases while that at {tex} B {/tex} and {tex} C {/tex} decreases
Intensity at {tex} A {/tex} and {tex} B {/tex} decreases, whereas intensity at {tex} C {/tex} increases
Intensity at {tex} A {/tex} and {tex} C {/tex} increases and that {tex} B {/tex} decreases
Intensity at {tex} A , B {/tex} and {tex} C {/tex} decreases
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Q 17. 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 } } \widehat { k } {/tex}
{tex} - \frac { 2 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}
{tex} \frac { 4 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}
{tex} - \frac { 4 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}
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Q 18. If the flux of the electric field through a closed surface is zero, then
The electric field must be zero everywhere on the surface
The total charge inside the surface must be zero
The electric field must be uniform throughout the closed surface
The charge outside the surface must be zero
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Q 19. Find the electric field vector at {tex} P ( a , a , a ) {/tex} due to three infinitely long lines of charges along the {tex} x - , y- {/tex} and {tex} z - {/tex} axis, respectively. The charge density, i.e., charge per unit length of each wire is {tex} \lambda {/tex}
{tex} \frac { \lambda } { 3 \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}
{tex} \frac { \lambda } { 2 \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}
{tex} \frac { \lambda } { 2 \sqrt { 2 } \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}
{tex} \frac { \sqrt { 2 } \lambda } { \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}
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Q 20. 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}
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Q 21. Let {tex} E _ { 1 } ( r ) , E _ { 2 } ( r ) {/tex} and {tex} E _ { 3 } ( r ) {/tex} be the respective electric field at a distance r from a point charge {tex} Q , {/tex} an infinitely long wire with constant lines chargedensity {tex} \lambda , {/tex} and an infinite plane with uniform surface charge density {tex} \sigma , {/tex} If {tex} E _ { 1 } \left( r _ { 0 } \right) = E _ { 2 } \left( r _ { 0 } \right) = E _ { 3 } \left( r _ { 0 } \right) {/tex} at a given distance {tex} r _ { 0 } , {/tex} then
{tex} Q = 4 \sigma \pi \mathrm { r } _ { 0 } ^ { 2 } {/tex}
{tex} r _ { 0 } = \frac { \lambda } { 2 \pi \sigma } {/tex}
{tex} E _ { 1 } \left( r _ { 0 } / 2 \right) = 2 E _ { 2 } \left( r _ { 0 } / 2 \right) {/tex}
{tex} E _ { 2 } \left( r _ { 0 } / 2 \right) = 4 E _ { 3 } \left( r _ { 0 } / 2 \right) {/tex}
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Q 22. A particle of charge {tex} - q {/tex} and mass {tex} m {/tex} moves in a circle of radius {tex}r{/tex} around an infinitely long line charge of linear charge density {tex} + \lambda {/tex}. Then time period will be
{tex} T = 2 \pi r \sqrt { \frac { m } { 2 k \lambda q } } {/tex}
{tex} T ^ { 2 } = \frac { 4 \pi ^ { 2 } m } { 2 k \lambda q } r ^ { 3 } {/tex}
{tex} T = \frac { 1 } { 2 \pi r } \sqrt { \frac { 2 k \lambda q } { m } } {/tex}
{tex} T = \frac { 1 } { 2 \pi r } \sqrt { \frac { m } { 2 \mathrm { k } \lambda q } } {/tex}
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Q 23. The electric dipole is situated is an electric field as shown in fig {tex} 1 . {/tex} The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to plane of paper passing through {tex}A{/tex} in anticlockwise direction. If the angle of rotation {tex} ( \theta ) {/tex} is measured with respect to the direction of electric field, then the torque {tex} ( \tau ) {/tex} experienced by the dipole for different values of the angle of rotation {tex} \theta {/tex} will be represented in fig. {tex} 2 , {/tex} by
curve(1)
curve(2)
curve(3)
curve(4)
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Q 24. A spherical conductor A contains two spherical cavities. The total charge on the conductor itself is zero. However, there is a point charge {tex} q _ { b } {/tex} at the centre of one cavity and {tex} q _ { c } {/tex} at the centre of the other.
A considerable distance {tex} r {/tex} away from the centre of the spherical conductor, there is another charge {tex} q _ { d } {/tex}, Force acting on {tex} q _ { b } , q _ { c } {/tex} and {tex} q _ { d } {/tex} are {tex} F _ { 1 } F _ { 2 } {/tex} and {tex} F _ { 3 } {/tex} respectively, then (Assume all charges are positive)
{tex} F _ { 1 } < F _ { 2 } < F _ { 3 } {/tex}
{tex} F _ { 1 } = F _ { 2 } < F _ { 3 } {/tex}
{tex} F _ { 1 } = F _ { 2 } > F _ { 3 } {/tex}
{tex} F _ { 1 } > F _ { 2 } > F _ { 3 } {/tex}
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Q 25. An electron with initial kinetic energy {tex} K _ { 0 } {/tex} is ejected at point {tex} A {/tex} as shown in the figure.
The acceleration of the electron (mass {tex} = \mathrm { m } _ { \mathrm { e } } {/tex} ) along y-axis is
{tex} \frac { 4 \pi \sigma e ^ { 2 } } { m _ { e } } {/tex}
{tex} \frac { - 4 \pi \sigma e } { m _ { e } } {/tex}
{tex} \frac { - 4 \pi e \sigma ^ { 2 } } { m _ { e } } {/tex}
{tex} \frac { - 4 \pi \sigma } { e m _ { e } } {/tex}
