IIT-JEE 2009 · Paper 1 · Physics Q47

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PhysicsSingle correct+3 / -1Question 47 of 60

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 $(a/4,-a/4,0)$ and $(-3a/4,3a/4,0)$ , respectively. Consider a cubical surface formed by six surfaces $x=\pm a/2$ , $y=\pm a/2$ , $z=\pm a/2$ . The electric flux through this cubical surface is

The x-y plane with the cube's square cross-section centred at the origin: a shaded disk centred on the left face (x = −a/2) on the x-axis, a thick rod along the x-axis starting inside the square and extending beyond its right edge, a point charge inside the square below the axis and another outside it at the upper left.

\dfrac{-2C}{\varepsilon_0}

\dfrac{2C}{\varepsilon_0}

\dfrac{10C}{\varepsilon_0}

\dfrac{12C}{\varepsilon_0}

Answer and worked solution

Official answer: A

Charge inside the cube ( $|x|,|y|,|z|\le\frac a2$ ):

the disk centred on the face $x=-\frac a2$ : half inside, $3C$ ;
the rod from $\frac a4$ to $\frac{5a}4$ : the part from $\frac a4$ to $\frac a2$ is a quarter of its length, $2C$ ;
$-7C$ at $\left(\frac a4,-\frac a4,0\right)$ : inside;
$3C$ at $\left(-\frac{3a}4,\frac{3a}4,0\right)$ : outside.

Gauss's law. $\Phi=\dfrac{3C+2C-7C}{\varepsilon_0}=\dfrac{-2C}{\varepsilon_0}$ .

(A)

Topics:Electric flux and Gauss's law

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IIT-JEE 2009 · Paper 1, Physics question 47