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NEET PHYSICSEasy

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0μC/m280.0 \, \mu\text{C/m}^2. The charge on the sphere is:

A

2.077×1032.077 \times 10^{-3} C

B

2.453×1032.453 \times 10^{-3} C

C

1.447×1031.447 \times 10^{-3} C

D

3.461×1033.461 \times 10^{-3} C

Step-by-Step Solution

The surface charge density σ\sigma is defined as charge per unit area (q/Aq/A). For a sphere, the surface area is A=4πR2A = 4\pi R^2. Given: Diameter d=2.4d = 2.4 m \Rightarrow Radius R=1.2R = 1.2 m Surface charge density σ=80.0μC/m2=80.0×106\sigma = 80.0 \, \mu\text{C/m}^2 = 80.0 \times 10^{-6} C/m2^2

Calculation: q=σ×4πR2q = \sigma \times 4\pi R^2 q=80.0×106×4×3.1416×(1.2)2q = 80.0 \times 10^{-6} \times 4 \times 3.1416 \times (1.2)^2 q=80.0×106×12.566×1.44q = 80.0 \times 10^{-6} \times 12.566 \times 1.44 q1447.6×106q \approx 1447.6 \times 10^{-6} C q=1.447×103q = 1.447 \times 10^{-3} C. (See NCERT Physics Class 12, Exercise 1.21).

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