(D) Given,electric field intensity $E = (2i + 3j + k) \ NC^{-1}$.Area vector $S = 10i \ m^2$.The electric flux $\phi$ through a surface is defined by

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(D) Given,electric field intensity $E = (2i + 3j + k) \ NC^{-1}$.Area vector $S = 10i \ m^2$.The electric flux $\phi$ through a surface is defined by the dot product of the electric field vector and the area vector:$\phi = E \cdot S$Substituting the given values:$\phi = (2i + 3j + k) \cdot (10i)$Since $i \cdot i = 1$,$j \cdot i = 0$,and $k \cdot i = 0$:$\phi = (2 \times 10) + (3 \times 0) + (1 \times 0)$$\phi = 20 \ Nm^2 C^{-1}$.

Class 12 Physics Electric Charges and Fields Electric Field Lines, Electric Flux and Gauss's Law

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In a region,the intensity of an electric field is given by $E = 2i + 3j + k$ in $NC^{-1}$. The electric flux through a surface $S = 10i \ m^2$ in the region is

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A
$5 \ Nm^2 C^{-1}$
B
$10 \ Nm^2 C^{-1}$
C
$15 \ Nm^2 C^{-1}$
D
$20 \ Nm^2 C^{-1}$

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Electric Charges and Fields

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Electric Field Lines, Electric Flux and Gauss's Law

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If electric flux through a cubic Gaussian surface is $1.9 \times 10^5 \text{ Nm}^2 \text{C}^{-1}$,then the electric charge at its center is . . . . . . . (Edge length of cube = $9.0 \text{ cm}$).

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$A$ uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu C/m^2$.
$(a)$ Find the charge on the sphere.
$(b)$ What is the total electric flux leaving the surface of the sphere?

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Two surfaces $S_1$ and $S_2$ are shown in the figure. The electric flux associated with $S_1$ is $\phi_1$ and with $S_2$ is $\phi_2$. Which of the following is correct?

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$A$ sphere of radius $R$ and charge $Q$ is placed inside a concentric imaginary sphere of radius $2R$. The flux associated with the imaginary sphere is

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$A$ point charge '$Q$' is placed at a point inside a hollow conducting sphere. Which of the following electric field patterns is correct?

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In a region,the intensity of an electric field is given by $E = 2i + 3j + k$ in $NC^{-1}$. The electric flux through a surface $S = 10i \ m^2$ in the region is

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If electric flux through a cubic Gaussian surface is $1.9 \times 10^5 \text{ Nm}^2 \text{C}^{-1}$,then the electric charge at its center is . . . . . . . (Edge length of cube = $9.0 \text{ cm}$).

$A$ uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu C/m^2$.$(a)$ Find the charge on the sphere.$(b)$ What is the total electric flux leaving the surface of the sphere?

Two surfaces $S_1$ and $S_2$ are shown in the figure. The electric flux associated with $S_1$ is $\phi_1$ and with $S_2$ is $\phi_2$. Which of the following is correct?

$A$ sphere of radius $R$ and charge $Q$ is placed inside a concentric imaginary sphere of radius $2R$. The flux associated with the imaginary sphere is

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$A$ uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu C/m^2$.
$(a)$ Find the charge on the sphere.
$(b)$ What is the total electric flux leaving the surface of the sphere?