Question

A uniform electric field E-3×10⁵NC^-1 is acting along the positive Y-axis. The electric flux through a rectangle of area 10cm × 30 cm whose plane is parallel to the Z-X plane is

• A. 12×10³ Vm
• B. 9×10³ Vm
• C. 15×10³ Vm
• D. 18×10³ Vm

Answer 1

The Correct Option is B

The given values are:

• The electric field: \( E = 3 \times 10^5 \, \text{N/C} \)
• The area of the rectangle: \( A = 10 \, \text{cm} \times 30 \, \text{cm} = 0.03 \, \text{m}^2 \)

Step 1: Formula for Electric Flux

The electric flux \( \Phi_E \) is given by the formula:

\[ \Phi_E = E \cdot A \cdot \cos(\theta) \]

Step 2: Calculation of the Electric Flux

The angle between the electric field and the normal to the surface is \( 0^\circ \), so \( \cos(0^\circ) = 1 \).

Now, substitute the known values into the formula:

\[ \Phi_E = 3 \times 10^5 \, \text{N/C} \times 0.03 \, \text{m}^2 \times 1 = 9 \times 10^3 \, \text{Vm} \]

The electric flux is \( 9 \times 10^3 \, \text{Vm} \), which corresponds to option (B).

Answer 2

The electric flux (φ) is given by the formula: \[ \phi = E \times A \times \cos \theta \] where \( \theta \) is the angle between the electric field and the area vector. Here, the area is 10 cm × 30 cm = 300 cm² = 300 × 10⁻⁴ m². Since the area plane is parallel to the Z-X plane, the angle between the electric field and the area vector is 0° (i.e., they are parallel). Thus, \[ \phi = E \times A = (3 \times 10^6) \times (300 \times 10^{-4}) = 9 \times 10^3 \, \text{Vm} \]