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Electrostatics

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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. 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 3. 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 4. 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 5. 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 6. 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 7. 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 8. 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 9. 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 10. 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 11. 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 12. 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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