Question

A disk of radius a/4 having a uniformly distributed charge -6C is placed in the x-y plane with its centre at (-a/2,0,0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (-a/4,0,0) and (-3a/4,3a/4,0), respectively. Consider a cubical surface formed by six surfaces x=± a/2, y=± a/2, z=± a/2. The electric flux through this cubical surface is 

• A. -(2C)/(varepsilon₀)
• B. (2C)/(varepsilon₀)
• C. (10C)/(varepsilon₀)
• D. (12C)/(varepsilon₀)

Hint:

For flux calculations, only the net enclosed charge matters — distribution and position inside do not affect the total flux.

Answer 1

The Correct Option is B

Step 1: By Gauss’s law: Φ = fracQₑₙclₒₛₑdvarepsilon₀ 

Step 2: Charges enclosed by the cube: 
• Part of the uniformly charged rod lies inside the cube ⟹ +2C 
• The disk lies completely outside the cube ⟹ 0 
• One point charge inside contributes accordingly 
• Net enclosed charge = 2C 

Step 3: Electric flux: Φ = (2C)/(varepsilon₀)