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
Using quantization of charge, \(q = ne ⇒ n = \frac{q}{e} = \frac{10^{-10}}{1.6 \times 10^{-19}} = 6.25 \times 10^8\).
Match column I and Column II.
**Column I**
(A) Coulomb’s law
(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
A matches with S (inverse square law), B with P (charge/area), C with R (\(q=ne\)), and D with Q (flux).
A neutral body is charged positively by rubbing it, its weight
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.
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
By quantization of charge, \(q = ne\). Solving for \(n\), we get \(n = \frac{q}{e} = \frac{10^{-10}\text{ C}}{1.6 \times 10^{-19}\text{ C}} = 6.25 \times 10^8\).
Assertion (A): Both the charge and mass are invariant.
Reason (R): Charge is always associated with mass.
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.
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.
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.
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.
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.
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.
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.
Assertion (A): We can shield a charge from electric fields by putting it inside a hollow conductor but we can not shield a body from the gravitational influence of near by matter by putting it inside a hollow sphere.
Reason (R): Gravitational force in between two point mass bodies is independent of the intervening medium them.
Assertion (A) is true: Electrostatic shielding (Faraday cage) works, but gravitational shielding does not. Reason (R) is true: Gravitational force is a fundamental interaction that is unaffected by the medium. (R) correctly explains (A) as electric fields can be screened by charge redistribution in conductors, a mechanism not available for gravity.
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.
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.