An electric field is given by E = (6i + 5j + 3k) N/C. The electric flux through a surface area 30i m^2 lying in the YZ-plane (in SI units) is:

Given: E = (6 i + 5 j + 3 k) N/C and A = 30 i m^2. Find: Electric flux through the given surface. Electric flux is given by the dot product: = E A Since the surface lies in the YZ-plane, its area vector is along i. Therefore, = (6 i + 5 j + 3 k) (30 i) Only the components along the same direction contribute in the dot product, so = 6 30 = 180 N m^2/ C Therefore, the electric flux through the surface is 180 N m^2/ C. The correct option is C.

An electric field is given by E = (6i + 5j + 3k) N/C. The electri… — Solution | JEE Physics

MCQEasyJEE 2024Gauss's Law Applications

An electric field is given by $E = (6i + 5j + 3k) \, \text{N/C}$ . The electric flux through a surface area $30i \, \text{m}^2$ lying in the $YZ$ -plane (in SI units) is:

A
$90$
B
$150$
C
$180$
D
$60$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: $\vec{E} = (6\hat{i} + 5\hat{j} + 3\hat{k}) \, \text{N/C}$ and $\vec{A} = 30\hat{i} \, \text{m}^2$ .

Find: Electric flux through the given surface.

Electric flux is given by the dot product:

\Phi = \vec{E} \cdot \vec{A}

Since the surface lies in the $YZ$ -plane, its area vector is along $\hat{i}$ . Therefore,

\Phi = (6\hat{i} + 5\hat{j} + 3\hat{k}) \cdot (30\hat{i})

Only the components along the same direction contribute in the dot product, so

\Phi = 6 \times 30 = 180 \, \text{N m}^2/\text{C}

Therefore, the electric flux through the surface is $180 \, \text{N m}^2/\text{C}$ . The correct option is C.

Common mistakes

Using the magnitude of the entire electric field vector instead of taking the dot product is incorrect, because flux depends only on the component normal to the surface. Use the area vector direction and compute $\vec{E} \cdot \vec{A}$ .
Assuming the area vector lies in the $YZ$ -plane is wrong, because the area vector is always perpendicular to the surface. For a surface in the $YZ$ -plane, the area vector is along $\hat{i}$ or $-\hat{i}$ .

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