(A) The electric flux $\phi$ through a surface is defined by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{A}$.Give

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(A) The electric flux $\phi$ through a surface is defined by the dot product of the electric field vector $\vec{E}$ and the area vector $\vec{A}$.Given $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$ and $\vec{A} = \pi R^2 \hat{i}$.$\phi = \vec{E} \cdot \vec{A} = (a \hat{i} + b \hat{j} + c \hat{k}) \cdot (\pi R^2 \hat{i})$.Since $\hat{i} \cdot \hat{i} = 1$,$\hat{i} \cdot \hat{j} = 0$,and $\hat{i} \cdot \hat{k} = 0$,we get:$\phi = a \cdot \pi R^2 = a \pi R^2$.

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

Easy

The electric field in a region is uniform and is given by $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$. The electric flux associated with a surface of area $\vec{A} = \pi R^2 \hat{i}$ is:

A
$a \pi R^2$
B
$3 a \pi R^2$
C
$2 a b R$
D
$a c R$

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Electric Charges and Fields

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Electric Field Lines, Electric Flux and Gauss's Law

$A$ metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric field lines?

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$q_1, q_2, q_3$ and $q_4$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?

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If the electric flux entering and leaving an enclosed surface are $\phi_1$ and $\phi_2$ respectively,the electric charge inside the surface will be

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$A$ charge $q$ is placed at the center of one of the faces of a cube. What is the electric flux linked with the cube?

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$A$ $6 \mu C$ charge is placed at the centre of a cube. What will be the electric flux through each face of the cube? (Take $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}$)

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The electric field in a region is uniform and is given by $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$. The electric flux associated with a surface of area $\vec{A} = \pi R^2 \hat{i}$ is:

Similar Questions

$A$ metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric field lines?

$q_1, q_2, q_3$ and $q_4$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?

If the electric flux entering and leaving an enclosed surface are $\phi_1$ and $\phi_2$ respectively,the electric charge inside the surface will be

$A$ charge $q$ is placed at the center of one of the faces of a cube. What is the electric flux linked with the cube?

$A$ $6 \mu C$ charge is placed at the centre of a cube. What will be the electric flux through each face of the cube? (Take $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}$)

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