JEE Advanced 2015 · Paper 1 · Physics Q1

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PhysicsInteger+4Question 1 of 60

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$ -axis in the $y$ - $z$ plane at $z=\dfrac{\sqrt3}{2}a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $ABCD$ lying in the $x$ - $y$ plane with its centre at the origin is $\dfrac{\lambda L}{n\varepsilon_0}$ ( $\varepsilon_0$ = permittivity of free space), then the value of $n$ is

Axes x, y, z with a rectangle ABCD in the x-y plane centred at the origin O: sides of length a along x (AD) and L along y (DC). A long line charge runs parallel to the y-axis at height (√3/2)a above the x-y plane, directly above the y-axis.

Your answer

Answer and worked solution

Official answer: 6

Geometry. The line charge sits at height $\frac{\sqrt3}2a$ directly above the $y$ -axis. The rectangle spans $|x|\le\frac a2$ . Seen from the line, each edge is at angle $\tan^{-1}\dfrac{a/2}{\sqrt3a/2}=30°$ from the vertical, so the rectangle subtends 60°.

Flux. Field lines leave the line charge radially and uniformly in angle. The total flux through a length $L$ is $\lambda L/\varepsilon_0$ , so the rectangle intercepts the fraction $60°/360°=\frac16$ :
$\Phi=\frac{\lambda L}{6\varepsilon_0}.$

Answer: 6

Topics:Electric flux and Gauss's law

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JEE Advanced 2015 · Paper 1, Physics question 1