Electric Field and Electric Field Lines

Electric Field and Electric Field Lines

Why does the electric field due to a uniformly charged wire drop off more slowly with distance compared to a point charg

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. The wire’s linear charge distribution leads to a cylindrical field pattern ( 1/r ), as per Gauss’s law, spreading over a surface area proportional to r . A point charge’s spherical spread ( 1/r² ) over r² results in a faster drop-off. Substituting values gives Linear distribution, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

A thin spherical shell of radius 31 cm has \( q = 20 \, \mu\text{C} \). What is the electric field at 35 cm from the cen

**Electric field** defined as E = F/q₀, force per unit positive test charge, unit N/C or V/m, direction along force on positive test charge. For point charge, E = k q/r² radially outward for q>0. Field lines start on positive and end on negative, density indicates strength. Outside shell: E = (k q/r²) . E = 9 × 10⁹ × (20 × 10⁻⁶/(0.35)²) = 9 × 10⁹ × (20 × 10⁻⁶/0.1225) = 1.469 × 10⁶ N/C . Substituting values gives 1.47 × 10⁶ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

A conducting sphere of radius 25 cm has an electric field of \( 2 \times 10^3 \, \text{N/C} \) at 50 cm from its center.

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. E = (k q/r²) . 2 × 10³ = 9 × 10⁹ × (q/(0.5)²) . q = (2 × 10³ × 0.25/9 × 10⁹) = 5.56 × 10⁻⁸ C . Substituting values gives 5.56 × 10⁻⁸ C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

A plane sheet has \( \sigma = 2.66 \times 10^{-11} \, \text{C/m}^2 \). What is the electric field near it?

**Field intensity** at distance r follows inverse-square law E = (1/4π ε₀)·q/r². At midpoint between two charges, fields superpose vectorially; if charges opposite, fields add in same direction, enhancing magnitude to E = E₁ + E₂. E = (sigma/2 ε₀) . E = (2.66 × 10⁻¹¹/2 × 8.854 × 10⁻¹²) = 1.5 N/C . Substituting values gives 1.5 N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency. This aligns with NCERT Class 11 treatment, emphasizing conservation, symmetry and dimensional consistency useful for CBSE, NEET and CUET.

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Electric Field and Electric Field Lines

A uniform electric field \( E = 2 \times 10^3 \, \text{N/C} \) is along the z-axis. What is the flux through a rectangle

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. Area vector Δ S = 0.3 × 0.5 = 0.15 m² along z-axis. Flux: Φ = E · Δ S = 2 × 10³ × 0.15 = 300 N·m²/C . Substituting values gives 300 N·m²/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

Why does the electric field due to an infinite charged sheet remain constant regardless of its thickness?

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. For an infinite sheet, Gauss’s law shows the field depends only on the surface charge density ( sigma/2ε₀ ). Thickness doesn’t affect the planar symmetry or enclosed charge per unit area, keeping the field constant. Substituting values gives Surface charge density, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

Which property of electric charges is responsible for the fact that charges on a conductor in equilibrium reside only on

**Electric field** defined as E = F/q₀, force per unit positive test charge, unit N/C or V/m, direction along force on positive test charge. For point charge, E = k q/r² radially outward for q>0. Field lines start on positive and end on negative, density indicates strength. In electrostatic equilibrium, the electric field inside a conductor must be zero. If charges existed inside, they would create a field, causing further movement. Thus, charges redistribute to the surface, where they can maintain zero internal field due to their mobility. Substituting values gives Mobility, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

What ensures that the electric field outside a neutral conductor in an external field is altered by induced charges?

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. Induced charge separation occurs as the external field polarizes the conductor, creating surface charges. These charges generate an additional field that superposes with the external field, modifying the total field outside the conductor. Substituting values gives Induced charge separation, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

Why does the torque on an electric dipole in a uniform field depend on the sine of the angle between the dipole and the

**Electric field** defined as E = F/q₀, force per unit positive test charge, unit N/C or V/m, direction along force on positive test charge. For point charge, E = k q/r² radially outward for q>0. Field lines start on positive and end on negative, density indicates strength. Torque ( tau = pE sin θ ) arises from the couple formed by forces on the dipole’s charges. The perpendicular component of the field to the dipole axis determines the rotational effect, which is maximum at 90° and zero when aligned (sin 0° = 0). Substituting values gives Perpendicular component, which matches expected magnitude for this electrostatic

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Electric Field and Electric Field Lines

A conducting sphere of radius 14 cm has an electric field of \( 7 \times 10^3 \, \text{N/C} \) at 28 cm from its center.

**Electric field concept** visualizes influence of source charge. Uniform field exerts constant force F = qE, and flux Φ = E·A = E A cosθ links field to area orientation, maximum when field normal to surface. E = (k q/r²) . 7 × 10³ = 9 × 10⁹ × (q/(0.28)²) . q = (7 × 10³ × 0.0784/9 × 10⁹) = 6.1 × 10⁻⁸ C . Substituting values gives 6.1 × 10⁻⁸ C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

Why does the electric field inside a charged insulator depend on the distribution of charges within it?

**Field intensity** at distance r follows inverse-square law E = (1/4π ε₀)·q/r². At midpoint between two charges, fields superpose vectorially; if charges opposite, fields add in same direction, enhancing magnitude to E = E₁ + E₂. Fixed charges in an insulator create a field based on their spatial arrangement. Gauss’s law shows the field at a point depends on the enclosed charge, which varies with position due to the immovable nature of the charges. Substituting values gives Charge distribution, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Field and Electric Field Lines

What fundamental concept explains why the electric field just outside a charged conductor is perpendicular to its surfac

**Electric field** defined as E = F/q₀, force per unit positive test charge, unit N/C or V/m, direction along force on positive test charge. For point charge, E = k q/r² radially outward for q>0. Field lines start on positive and end on negative, density indicates strength. In electrostatic equilibrium, the electric field inside a conductor is zero. If the field just outside had a tangential component, charges would move along the surface, contradicting equilibrium. Thus, the field must be normal to the surface. Substituting values gives Electrostatic equilibrium, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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