Q25. A uniformly charged conducting sphere of radius 1.3 m has a surface charge density of 70 µC m-2

Q: What is the correct answer for CUET UG Physics Q25?

The correct answer is c. According to Gauss's Law, the total electric flux (Φ_total) leaving any closed surface (a Gaussian surface) is given by Φ_total = Q_enclosed / ε₀, where Q_enclosed is the total charge enclosed within the surface, and ε₀ is the permittivity of free space (ε₀ ≈ 8.854 × 10⁻¹² C²/(N·m²)). For a uniformly charged conducting sphere of radius r = 1.3 m, with a surface charge density σ = 70 µC/m² = 70 × 1

Q: Q25. A uniformly charged conducting sphere of radius 1.3 m has a surface charge density of 70 µC m-2. What is the total electric flux leaving the surface of the sphere? (a) 5.9 x 108 N m² C-1 (b) 1.7…

The correct answer is c. According to Gauss's Law, the total electric flux (Φ_total) leaving any closed surface (a Gaussian surface) is given by Φ_total = Q_enclosed / ε₀, where Q_enclosed is the total charge enclosed within the surface, and ε₀ is the permittivity of free space (ε₀ ≈ 8.854 × 10⁻¹² C²/(N·m²)). For a uniformly charged conducting sphere of radius r = 1.3 m, with a surface charge density σ = 70 µC/m² = 70 × 1

Q: What are the options for this CUET UG Physics question?

A. 5.9 x 10⁸ N m² C⁻¹ · B. 1.7 x 10⁻⁸ N m² C⁻¹ · C. 1.7 x 10⁸ N m² C⁻¹ · D. 6.4 x 10⁻⁸ N m² C⁻¹

Question

Q25. A uniformly charged conducting sphere of radius 1.3 m has a surface charge density of 70 µC m-2. What is the total electric flux leaving the surface of the sphere?
(a) 5.9 x 108 N m² C-1
(b) 1.7 x 10-8 N m² C-1
(c) 1.7 x 108 N m² C-1
(d) 6.4 x 10-8 N m² C-1

FirstInTest · Accepted Answer

According to Gauss's Law, the total electric flux (Φ_total) leaving any closed surface (a Gaussian surface) is given by Φ_total = Q_enclosed / ε₀, where Q_enclosed is the total charge enclosed within the surface, and ε₀ is the permittivity of free space (ε₀ ≈ 8.854 × 10⁻¹² C²/(N·m²)). For a uniformly charged conducting sphere of radius r = 1.3 m, with a surface charge density σ = 70 µC/m² = 70 × 10⁻⁶ C/m², the total charge Q_enclosed on its surface is Q = σ × (surface area) = σ × 4πr². So, Q = (70 × 10⁻⁶ C/m²) × 4π × (1.3 m)² ≈ 1.48 × 10⁻³ C. Now, calculate the total electric flux: Φ_total = (1.48 × 10⁻³ C) / (8.854 × 10⁻¹² C²/(N·m²)) ≈ 1.67 × 10⁸ N m²/C. Rounding to two significant figures, this is 1.7 × 10⁸ N m²/C. Options (a), (b), and (d) are incorrect due to calculation errors or incorrect orders of magnitude.

Answer

5.9 x 10⁸ N m² C⁻¹

Answer

1.7 x 10⁻⁸ N m² C⁻¹

Answer

1.7 x 10⁸ N m² C⁻¹

Answer

6.4 x 10⁻⁸ N m² C⁻¹

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