if a cube is given with length l and we have a long wire with charge density lambda then

Question

if a cube is given with length l and we have a long wire with charge density lambda then what will be the length of wire for maximum electric flux also find the maximum electric flux

Answer 1

By Gauss' law, the flux through the surface of the cube is just the the total enclosed charge divided by the electric permitivity.

 

Φ = Q/ε₀ 

 

To maximize Φ, just maximize Q.  But

 

Q_max= λr,

 

where r is the maximum length of wire that fits inside the cube.  If the length of the cube is L, then

 

r = √(3L²) = (√3)L

 

Then

 

Φ_max = (√3)Lλ / ε₀