A line charge of length is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is C per unit length, then the total electric flux through al the faces of the cube will be _____

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A line charge of length $\frac{' a'}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is $λ$ C per unit length, then the total electric flux through all the faces of the cube will be ______ (Take, $ε_{0}$ as the free space permittivity) [2025]

1 $\frac{λ a}{8 ε_{0}}$

2 $\frac{λ a}{16 ε_{0}}$

3 $\frac{λ a}{2 ε_{0}}$

4 $\frac{λ a}{4 ε_{0}}$

Ans.
(1)

Charge of the line charge $= \frac{a λ}{2}$

Portion of wire inside cube $= \frac{1}{4}$

Total charge inside the cube, $q_{en} = \frac{1}{4} (\frac{a λ}{2}) = \frac{λ a}{8}$

$∴ ϕ = \frac{q_{en}}{ε_{0}} = \frac{λ a}{8 ε_{0}}$

Want Us to Email you About Special Offers & Updates?