A point charge causes an electric flux of to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given ) [2025]

Question

A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2025]

Smart Achievers · Accepted Answer

(1)

$ϕ = - 2 \times 10^{4} \frac{{Nm}^{2}}{C}$

$ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$

$\Rightarrow q = ε_{0} ϕ = (8.85 \times 10^{- 12}) \times (- 2 \times 10^{4})$

$q = - 17.7 \times 10^{- 8} C$

Solution

Q.
A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2025]

1 $- 17.7 \times 10^{- 8} C$

2 $- 15.7 \times 10^{- 8} C$

3 $17.7 \times 10^{- 8} C$

4 $15.7 \times 10^{- 8} C$

Ans.
(1)

$ϕ = - 2 \times 10^{4} \frac{{Nm}^{2}}{C}$

$ϕ = \frac{q}{ε_{0}}$

$\Rightarrow q = ε_{0} ϕ = (8.85 \times 10^{- 12}) \times (- 2 \times 10^{4})$

$q = - 17.7 \times 10^{- 8} C$

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Solution

Q. A point charge causes an electric flux of –2×104 Nm2C–1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given ε0=8.85×10–12C2N–1m–2) [2025]

1 –17.7×10–8 C

2 –15.7×10–8 C

3 17.7×10–8 C

4 15.7×10–8 C

Ans. (1) ϕ=–2×104Nm2C ϕ=qε0 ⇒ q=ε0ϕ=(8.85×10–12)×(–2×104) q=–17.7×10–8C