JEE Mains · Physics · STD 12 - 1. Electric charges and fields
A line charge of length \(\frac{\text { ' } a \text { ' }}{2}\) is kept at the center of an edge \(B C\) of a cube \(A B C D E F G H\) having edge length ' \(a\) ' as shown in the figure. If the density of line charge is \(\lambda\) C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, \(\epsilon_0\) as the free space permittivity)
- A \(\frac{\lambda \mathrm{a}}{2 \epsilon_0}\)
- B \(\frac{\lambda \mathrm{a}}{4 \epsilon_0}\)
- C \(\frac{\lambda \mathrm{a}}{16 \epsilon_0}\)
- D \(\frac{\lambda \mathrm{a}}{8 \epsilon_0}\)
Answer & Solution
Correct Answer
(D) \(\frac{\lambda \mathrm{a}}{8 \epsilon_0}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Charge of the line charge }=\frac{a \lambda}{2} \\ & \text { Portion of wire inside cube }=\frac{1}{4} \\ & \therefore \quad q_{e n}=\frac{1}{4}\left(\frac{a \lambda}{2}\right)=\frac{a \lambda}{8} \\ & \qquad \phi=\frac{q_{e n}}{\varepsilon_0}=\frac{a…
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