Question

In a region of space having a uniform electric field \( E \), a hemispherical bowl of radius \( r \) is placed. The electric flux \( \Phi \) through the bowl is:

• A. \( 2 \pi r^2 E \)
• B. \( 4 \pi r^2 E \)
• C. \( 2 r^2 E \)
• D. \( \pi r^2 E \)

Hint:

Electric flux through a hemispherical surface can be calculated using \( \Phi = E \cdot A \), where the area of the hemisphere is \( 2 \pi r^2 \).

Answer 1

The Correct Option is C

Step 1: Electric flux definition.
Electric flux \( \Phi \) through a surface is given by: \[ \Phi = E \cdot A \cos \theta \] where \( E \) is the electric field and \( A \) is the area of the surface.

Step 2: Apply the formula for hemispherical bowl.
For a hemispherical bowl, the surface area is \( A = 2\pi r^2 \). Therefore, the electric flux through the bowl is \( 2 r^2 E \). Thus, the correct answer is (3).