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NEET PHYSICSEasy

A point charge of 2.0μC2.0 \, \mu\text{C} is at the center of a cubic Gaussian surface 9.0cm9.0 \, \text{cm} on edge. What is the net electric flux through the surface?

A

2.26×105N m2C12.26 \times 10^5 \, \text{N m}^2 \text{C}^{-1}

B

2.09×105N m2C12.09 \times 10^5 \, \text{N m}^2 \text{C}^{-1}

C

4.33×105N m2C14.33 \times 10^5 \, \text{N m}^2 \text{C}^{-1}

D

4.71×105N m2C14.71 \times 10^5 \, \text{N m}^2 \text{C}^{-1}

Step-by-Step Solution

According to Gauss's Law, the net electric flux ΦE\Phi_E through a closed surface depends only on the net charge enclosed (qq) and the permittivity of free space (ε0\varepsilon_0), independent of the size or shape of the surface. Formula: ΦE=qε0\Phi_E = \frac{q}{\varepsilon_0} Given: q=2.0μC=2.0×106Cq = 2.0 \, \mu\text{C} = 2.0 \times 10^{-6} \, \text{C} ε08.854×1012C2N1m2\varepsilon_0 \approx 8.854 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} Calculation: ΦE=2.0×1068.854×10120.2258×106=2.26×105N m2C1\Phi_E = \frac{2.0 \times 10^{-6}}{8.854 \times 10^{-12}} \approx 0.2258 \times 10^6 = 2.26 \times 10^5 \, \text{N m}^2 \text{C}^{-1}. (See NCERT Physics Class 12, Exercise 1.18).

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