Physics - Electrostatic Potential Capacitance - Quiz-9

A parallel plate capacitor is charged to a certain potential difference. A slab of thickness 3 mm is inserted between the plates and it becomes necessary to increase the distance between the plates by 2.4 mm to maintain the same potential difference. The dielectric constant of the slab is–

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3
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5
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2.5
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2

A charge $Q$ is distributed over two concentric hollow spheres of radii r and $R (R > r)$ such that the surface densities are equal. The potential at the common centre is $\frac{1}{4 {πε}_{0}}$ times –

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$Q (\frac{r + R}{r^{2} + R^{2}})$
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$\frac{Q}{2} (\frac{r + R}{r^{2} + R^{2}})$
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$2 Q (\frac{r + R}{r^{2} + R^{2}})$
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Zero

A charge $+ Q$ is uniformly distributed over a thin ring of radius $R$ , velocity of an electron at the moment it passes through the centre $O$ of the ring, if the electron was initially at rest at a point $A$ which is very far away from the centre and on the axis of the ring is

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$\sqrt{\frac{2 kQe}{mR}}$
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$\sqrt{\frac{kQe}{m}}$
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$\sqrt{\frac{kme}{QR}}$
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$\sqrt{\frac{kQe}{mR}}$

The electric potential V as a function of distance x (in metre) is given by: $V = (5 x^{2} + 10 x - 9) V .$ The value of the electric field of x = 1m would be -

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$20 V / m$
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$6 V / m$
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$11 V / m$
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$- 23 V / m$

In a region, the electric field intensity E is given by $E = 100 / x^{2}$ where x is in metre. The potential difference between the points at $x = 10 m$ and $x = 20 m$ will be :

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$1 V$
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$2 V$
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$5 V$
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$10 V$

An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of $V_{0}$ . If the common potential after sharing of charges becomes $V$ , then the dielectric constant of the dielectric must be –

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$\frac{V_{0}}{V}$
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$\frac{V}{V_{0}}$
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$\frac{V_{0} - V}{V}$
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$\frac{V_{0} - V}{V_{0}}$

Two parallel conducting plates $5 mm$ apart are held horizontally one above the other. The upper plate is maintained at a positive potential of $15 kV$ while the lower plate is earthed. If a small oil drop of relative density $0.92$ and of radius $5 µ m$ remains stationary between the plates, then the charge on the drop will be.

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$10 e$
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$8 e$
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$5 e$
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$3 e$

An infinite number of charges (each of magnitude $1 µ c$ ) are placed along the $X$ -axis at x = 1, 2, 4, 8....metre. If the charges are alternately of opposite sign, then the potential at the point x = 0 due to these charges will be.

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$6 \times 10^{3} V$
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$9 \times 10^{3} V$
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$1.8 \times 10^{4} V$
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$1.2 \times 10^{4} V$

Figure shows a ball having a charge q fixed at a point $A$ . Two identical balls having charges +q and –q and mass ‘m’ each are attached to the ends of a light rod of length $2 a$ . The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid-point of the rod. The system is released from the situation shown in figure. Find the angular velocity of the rod when the rod becomes horizontal.

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$\frac{\sqrt{2} q}{3 π \in_{0} {ma}^{3}}$
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$\frac{q}{\sqrt{3 π \in_{0} {ma}^{3}}}$
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$\frac{q}{\sqrt{6 π \in_{0} {ma}^{3}}}$
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$\frac{\sqrt{2} q}{4 π \in_{0} {ma}^{3}}$

A proton and an $α$ -particle are at a distance r from each other. After letting them free if they move to infinity, the kinetic energy of the proton will be -

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$8 {Ke}^{2} / 5 r$
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$2 {Ke}^{2} / 5 r$
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$8 {Ke}^{2} / r$
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${Ke}^{2} / 5 r$

$10^{3}$ small water drops, each of radius r and each carrying charge q, combine to form one bigger drop. The potential of a bigger drop as compared to that of a smaller drop will be.

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$10^{5} V$
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$10^{3} V$
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$10 V$
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$10^{2} V$

The plates of a parallel plate capacitor have an area of $90 {cm}^{2}$ each and are separated by $2.5 mm$ . The capacitor is charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?

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$2.55 \times 10^{- 6} J$
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$1.55 \times 10^{- 6} J$
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$8.15 \times 10^{- 6} J$
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$5.5 \times 10^{- 6} J$

An alpha particle with kinetic energy $10 MeV$ is heading towards a stationary nucleus of atomic number $50$ . Calculate the distance of closest approach.

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$1.4 \times 10^{- 15} m$
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$4 \times 10^{- 15} m$
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$14.4 \times 10^{- 15} m$
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$8 \times 10^{- 15} m$

Calculate the area of the plates of a one farad parallel plate capacitor if the separation between plates is $1 mm$ and plates are in a vacuum.

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$18 \times 10^{8} m^{2}$
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$0.3 \times 10^{8} m^{2}$
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$1.3 \times 10^{8} m^{2}$
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$1.13 \times 10^{8} m^{2}$

A solid conducting sphere of radius a having a charge $q$ is surrounded by a concentric conducting spherical shell of inner radius $2 a$ and outer radius $3 a$ as shown in figure.

Find the amount of heat produced when switch is closed.

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${Kq}^{2} / 2 a$
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${Kq}^{2} / 3 a$
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${Kq}^{2} / 4 a$
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${Kq}^{2} / 6 a$

A parallel plate capacitor of area ‘A’ , plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement ?

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$\frac{3 {Kε}_{0} A}{4 d}$
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$\frac{4 {Kε}_{0} A}{3 d}$
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$\frac{(K + 1) ε_{0} A}{2 d}$
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$\frac{K (K + 3) ε_{0} A}{2 (K + 1) d}$

A capacitor of 2 µF is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:

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20%
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Assertion : A particle $A$ of mass m and charge $Q$ moves directly towards a fixed particle $B$ , which

has charge $Q$ . The speed of $A$ is $v$ when it is far away from $B$ . The minimum separation

between the particles is proportional to $Q^{2}$ .

Reason : Total energy remains conserved.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : Potential difference between two points lying in a uniform electric field may be equal

to zero.

Reason : Points of line normal to electric field is equipotential line.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : At a distance r from a +ve charged particle potential is V and electric field strength is E.

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Then grph between $V^{2}$ & $E$ is straight line.
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Reason : For a point charge $\frac{V^{2}}{E} = \frac{q}{4 π \in_{0}}$
1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

Assertion : Electrons move away from a region of lower potential to a region of higher potential.

Reason : Since an electron has a negative charge.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : Charges are given to plates of two plane parallel plate capacitors $C_{1}$ and $C_{2}$ (such

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that $C_{2} = 2 C_{1}$ ) as shown in figure. Then the key $K$ is pressed to complete the circuit.
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Finally the net charge on upper plate and net charge on lower plate of capacitor $C_{1}$ is positive.
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Reason : In a parallel plate capacitor both plates always carry equal and opposite charge.
1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

Assertion : Each of the plates of a parallel-plate capacitor is given equal positive charge Q. The

charges on the facing surfaces will be same.

Reason : A negative charge (–Q) will be induced on each of the facing surfaces.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : Electric potential is a property of an electric field, regardless of whether a charged

object has been placed in that field.

Reason : Potential depends on test charge.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : Electric potential and electric potential energy are different quantities.

Reason : For a system of positive test charge and point charge electric potential energy = electric potential.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : The component of $\vec{E}$ in any direction is the negative of the rate of change of the

electric potential with distance in that direction.

Reason : Potential gradient in any direction at a point gives total electric field at that point.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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Assertion : Two equipotential surfaces cannot cut each other.

Reason : Two equipotential surfaces are parallel to each other.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

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The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A is:

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independent of the distance between the plates.
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linearly proportional to the distance between the plates.
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proportional to the square root of the distance between the plates.
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inversely proportional to the distance between the plates.

If potential [in volts] in a region is expressed as V [x, y, z] = 6xy- y + 2yz, the electric field [in N/C] at point [1, 1, 0] is -

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$- (3 \hat{i} + 5 \hat{j} + 3 \hat{k})$
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$- (6 \hat{i} + 5 \hat{j} + 2 \hat{k})$
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$- (2 \hat{i} + 3 \hat{j} + \hat{k})$
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$- (6 \hat{i} + 9 \hat{j} + \hat{k})$

A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is?

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$\frac{C^{2} V^{2}}{2 d}$
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$\frac{C V^{2}}{2 d}$
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$\frac{C V^{2}}{d}$
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$\frac{C^{2} V^{2}}{2 d^{2}}$

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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