IIT-JEE 2012 · Paper 1 · Physics Q11

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PhysicsMultiple correct+4Question 11 of 60

A cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a/4,0)$ , $+3q$ at $(0,0,0)$ and $-q$ at $(0,+a/4,0)$ . Choose the correct option(s).

A cube of side a centred at the origin with x, y, z axes; charges −q at (0, −a/4, 0), 3q at the origin and −q at (0, a/4, 0) lie along the y-axis.

The net electric flux crossing the plane

x=+a/2

is equal to the net electric flux crossing the plane

x=-a/2

The net electric flux crossing the plane

y=+a/2

is more than the net electric flux crossing the plane

y=-a/2

The net electric flux crossing the entire region is

\dfrac q{\varepsilon_0}

The net electric flux crossing the plane

z=+a/2

is equal to the net electric flux crossing the plane

x=+a/2

Answer and worked solution

Official answer: A, C, D

Total flux. The enclosed charge is $-q+3q-q=q$ , so the flux through the whole cube is $q/\varepsilon_0$ . (C) true.

Symmetry. All charges lie on the $y$ axis, symmetric about the origin.

(A) The faces $x=\pm a/2$ are mirror images: equal flux. True.
(B) The faces $y=\pm a/2$ are mirror images too (the charge arrangement is symmetric under $y\to-y$ ): equal flux, not more. False.
(D) Rotating about the $y$ axis by 90° maps the face $z=+a/2$ to $x=+a/2$ and leaves the charges unchanged: equal flux. True.

(A), (C), (D)

Topics:Electric flux and Gauss's law

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IIT-JEE 2012 · Paper 1, Physics question 11