Electrostatics

Practice Questions:

Question 161: easy

The electric field in a region is directed outward and is proportional to the distance \(r\) from the origin. If we take a spherical volume of radius \(r\) taking centre at the origin, then the charge contained inside the volume is proportional to

1. \(r\)

2. \(r^2\)

3. \(r^0\)

4. \(r^3\)

View Answer

From Gauss's Law, the enclosed charge is proportional to the electric flux: \(q \propto E \cdot A\). Since \(E \propto r\) and area \(A \propto r^2\), we get \(q \propto r \cdot r^2 = r^3\).

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Question 162: easy

A neutral body is charged positively by rubbing it, its weight

1. Increases slightly

2. Decreases slightly

3. Remains constant

4. May increase or decrease

View Answer

When a neutral body is charged positively, it loses electrons. Since electrons have a finite mass \((m_e \approx 9.1 \times 10^{-31}\text{ kg})\), the loss of electrons results in a slight decrease in its mass and weight.

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Question 163: easy

The number of electrons that should be removed from a metal coin such that coin acquires a positive charge of \(10^{-10}\text{ C}\) is

1. \(1.6 \times 10^{-19}\)

2. \(6.25 \times 10^9\)

3. \(6.25 \times 10^8\)

4. \(1.6 \times 10^8\)

View Answer

By quantization of charge, \(q = ne\). Solving for \(n\), we get \(n = \frac{q}{e} = \frac{10^{-10}\text{ C}}{1.6 \times 10^{-19}\text{ C}} = 6.25 \times 10^8\).

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Question 164: easy

Sixty four identical drops of water having equal charge combine to form a bigger drop. The factor by which potential of bigger drop change in comparison to a small drop is

1. 64

2. 32

3. 16

4. 8

View Answer

By conserving volume, \(R = n^{1/3}r = 64^{1/3}r = 4r\). The total charge is \(Q = 64q\). Thus, potential of the big drop is \(V' = \frac{kQ}{R} = \frac{64kq}{4r} = 16V\).

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Question 165: easy

Match column I and Column II.

**Column I**(A) Coulomb’s lawn(B) Surface charge density (C) Quantisation of charge (D) Electric flux

**Column II**(P) Charge/Area (Q) \( \oint \vec{E} \cdot d\vec{s} \) (R) \( q = ne \) (S) Force is inversely proportional to square of distance

1. A \( \rightarrow \) P, B \( \rightarrow \) Q, C \( \rightarrow \) R, D \( \rightarrow \) S

2. A \( \rightarrow \) S, B \( \rightarrow \) P, C \( \rightarrow \) R, D \( \rightarrow \) Q

3. A \( \rightarrow \) S, B \( \rightarrow \) R, C \( \rightarrow \) P, D \( \rightarrow \) Q

4. A \( \rightarrow \) S, B \( \rightarrow \) P, C \( \rightarrow \) Q, D \( \rightarrow \) R

View Answer

Coulomb's law is an inverse square law (A-S). Surface charge density is charge per unit area (B-P). Charge is quantised as \( q=ne \) (C-R). Electric flux is defined by Gauss's integral (D-Q).

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Question 166: easy

Assertion (A): The tyres of aircrafts are slightly conducting.

Reason (R): If a conductor is connected to ground, the extra charge induced on conductor will flow to ground.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is true: Aircraft tyres are made slightly conducting to discharge static electricity accumulated during flight.nReason (R) is true: Grounding allows excess charge to flow to Earth.

(R) correctly explains (A) as the purpose of conducting tyres is to discharge static charge to the ground safely.

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Question 167: easy

Assertion (A): Both the charge and mass are invariant.

Reason (R): Charge is always associated with mass.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is true, considering 'mass' as rest mass, which is invariant, similar to charge. Reason (R) is true: All charged particles possess mass; a massless particle cannot carry charge.

(R) is not the correct explanation for (A), as invariance of charge and rest mass are fundamental properties, not directly explained by their association.

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Question 168: easy

Assertion (A): The electric field due to a charge configuration with total charge zero may not be zero.

Reason (R): Electric field obeys the principle of superposition.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is true: An electric dipole has zero net charge but produces a non-zero electric field. Reason (R) is true: Electric fields add vectorially due to superposition. (R) correctly explains (A) because individual fields from component charges, even if their sum is zero, combine vectorially to form a net non-zero field.

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Question 169: easy

Assertion (A): Vehicles carrying highly inflammable materials have hanging chains, slightly touching the ground.

Reason (R): The body of a vehicle gets charged when moving through air at high speed.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is true: These chains are a safety measure to discharge static electricity. Reason (R) is true: Friction between the vehicle's body and air (or tires and road) generates static charge.

(R) correctly explains (A) as the chains provide a path to ground, preventing dangerous sparks from static charge buildup.

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Question 170: easy

Assertion (A): The tyres of aeroplanes are slightly conducting.

Reason (R): During take off and landing of aeroplanes, the friction between tyres and the runway may cause electrification of tyres.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Assertion (A) is true: Conducting tyres prevent hazardous static charge accumulation. Reason (R) is true: Friction during takeoff and landing causes static electrification.

(R) correctly explains (A) because the conducting tyres allow the generated static charge to safely discharge into the runway, preventing sparks and potential ignitions.

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