JEE Advanced · Physics · 17. Electrostatics
A cubical region of side \(a\) has its centre at the origin. It encloses three fixed point charges, \(-q\) at \((0,-a / 4,0),+3 q\) at \((0,0,0)\) and \(-q\) at \((0,+a / 4,0)\). Choose the correct options(s)
- A The net electric flux crossing the plane \(x=+a / 2\) is equal to the net electric flux crossing the plane \(x=-\) \(a / 2\)
- B The net electric flux crossing the plane \(y=+a / 2\) is more than the net electric flux crossing the plane \(y=-a / 2\).
- C The net electric flux crossing the entire region is \(\frac{q}{\varepsilon_{0}}\)
- D The net electric flux crossing the plane \(z=+a / 2\) is equal to the net electric flux crossing the plane \(x=+a / 2\).
Answer & Solution
Correct Answer
(A) The net electric flux crossing the plane \(x=+a / 2\) is equal to the net electric flux crossing the plane \(x=-\) \(a / 2\)
Step-by-step Solution
Detailed explanation
Due to symmetry, the net electric flux passing through \(x=+\frac{a}{2}\), \(x=-\frac{a}{2}, z=+\frac{a}{2}\) is same
According to Gauss's theorem, net electric flux net electric flux crossing through any closed surface \(\phi=\frac{q_{\text {in }}}{\varepsilon_{0}}=\) \(\frac{-q+3 q-q}{\varepsilon_{0}}=\frac{q}{\varepsilon_{0}}\).
According to Gauss's theorem, net electric flux net electric flux crossing through any closed surface \(\phi=\frac{q_{\text {in }}}{\varepsilon_{0}}=\) \(\frac{-q+3 q-q}{\varepsilon_{0}}=\frac{q}{\varepsilon_{0}}\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two non-conducting spheres of radii and and carrying uniform volume charge densities and , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
JEE Advanced 2013 Hard - A police car with a siren of frequency \(8 \mathrm{kHz}\) is moving with uniform velocity \(36 \mathrm{~km} / \mathrm{h}\) towards a tall building which reflects the sound waves. The speed of sound in air is \(320 \mathrm{~m} / \mathrm{s}\). The frequency of the siren heard by the car driver isJEE Advanced 2011 Easy
- Two identical glass rods and (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light is placed inside rod on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside . The distance is
JEE Advanced 2015 Hard - In the Young's double slit experiment using a monochromatic light of wavelength , the path difference ( in terms of an integer ) corresponding to any point having half the peak intensity isJEE Advanced 2013 Medium
- \(5.6 \mathrm{~L}\) of helium gas at STP is adiabatically compressed to \(0.7 \mathrm{~L}\). Taking the initial temperature to be \(T_1\), the work done in the process isJEE Advanced 2011 Hard
- Paragraph :
\(P_{14-16}\) : Paragraph for Questions Nos. 14 to 16 A fixed thermally conducting cylinder has a radius \(R\) and height \(L_0\). The cylinder is open at its bottom and has a small hole at its top. A piston of mass \(M\) is held at a distance \(L\) from the top surface as shown in the figure. The atmospheric pressure is \(p_0\).
Question :
While the piston is at a distance \(2 L\) from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top isJEE Advanced 2007 Hard
More PYQs from JEE Advanced
- A horizontal forceis applied at the centre of mass of a cylindrical object of massand radius, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is. The centre of mass of the object has an acceleration. The acceleration due to gravity is. Given that the object rolls without slipping, which of the following statement(s) is (are) correct?
JEE Advanced 2021 Hard - A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg . Suppose that the variation of the height \(y\) (in m ) of the elevator, from the ground, with time \(t\) (in s ) is given by \(y=8\left[1+\sin \left(\frac{2 \pi t}{T}\right)\right]\), where \(T=40 \pi \mathrm{~s}\). Taking acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), the maximum variation of the object's weight (in N ) as observed in the experiment is _______ .JEE Advanced 2025 Medium
- Consider an obtuse angled triangle in which the difference between the largest and the smallest angle is and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius .
(There are two questions based on , the question given below is one of them)
Then the inradius of the triangle isJEE Advanced 2023 Medium - Four persons independently solve a certain problem correctly with probabilities . Then the probability that the problem is solved correctly by at least one of them isJEE Advanced 2013 Medium
- Thermal decomposition of produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _____ .JEE Advanced 2022 Easy
- A uniform capillary tube of inner radius is dipped vertically into a beaker filled with water. The water rises to a height in the capillary tube above the water surface in the beaker. The surface tension of water is . The angle of contact between water and the wall of the capillary tube is . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?JEE Advanced 2018 Medium