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NEET PHYSICSEasy

The electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0×1038.0 \times 10^3 Nm2^2/C. What is the net charge inside the box?

A

1.01 \mu C

B

0.01 \mu C

C

0.03 \mu C

D

0.07 \mu C

Step-by-Step Solution

According to Gauss's Law, the net electric flux ΦE\Phi_E through a closed surface is equal to the net charge qq enclosed divided by the permittivity of free space ε0\varepsilon_0 (ΦE=q/ε0\Phi_E = q/\varepsilon_0). Given: ΦE=8.0×103\Phi_E = 8.0 \times 10^3 Nm2^2/C ε08.854×1012\varepsilon_0 \approx 8.854 \times 10^{-12} C2^2/Nm2^2

Calculation: q=ΦE×ε0q = \Phi_E \times \varepsilon_0 q=(8.0×103)×(8.854×1012)q = (8.0 \times 10^3) \times (8.854 \times 10^{-12}) q=70.832×109q = 70.832 \times 10^{-9} C q0.07×106q \approx 0.07 \times 10^{-6} C =0.07= 0.07 \mu C. (See NCERT Physics Class 12, Exercise 1.16).

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