Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainPhysicsElectrostatics

A thin non-conducting circular disc of radius R has a uniform surface charge density . It is placed such that its center exactly coincides with the midpoint of an edge of a cube of side length a (where a > 2R ). The plane of the disc is perpendicular to that edge. The total electric flux through all the faces of the cube is (Take ₀ as the permittivity of free space)

Options

  1. AR^2 4 ₀
  2. BR^2 2 ₀
  3. CR^2 8 ₀
  4. DR^2 ₀

Correct answer

A. R^2 4 ₀

Step-by-step solution

The total charge on the disc is q = R^2 . The edge of a cube is formed by the intersection of two faces at an angle of 90^ . Since the disc is centered on the edge and its plane is perpendicular to the edge, exactly a 90^ sector of the disc lies inside the volume of the cube. Therefore, the fraction of the disc's area (and hence its charge) enclosed by the cube is 90^ 360^ = 1 4 . Enclosed charge, q_ en = R^2 4 . By Gauss's Law, the total electric flux through the cube is = q_ en ₀ = R^2 4 ₀ . Answer: R^2 4 ₀

Practice Electrostatics on Quantrex Academy →

More from Electrostatics

Two charges Q₁ = q and Q₂ = mq are placed at the points P₁(a, b) and P₂(ma, mb) , respectively, in the XY plane, where a, b 0 and m 0, 1 . If V₁ is the potential at a point in the 2026Consider an electric dipole comprising two charges +q and -q each with mass m , separated by a fixed distance d and initially at rest with its dipole moment pointing along i . A un 2026Two point charges q₁=3 , C and q₂=-4 , C are placed at points (2 i +3 j +3 k ) and ( i + j + k ) respectively. Force on charge q₂ is ________ N. ( Take 1 4 ₀ = 9 10^9 SI Units ) 2026The electric potential as a function of x, y is given by V = 5(x^2 - y^2) V. The electric field at a point (2, 3) m is __________ V/m. 2026A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value 2026A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E = 2x i + 3y^2 j + 4 k N/C. The work done in moving the charge is 2026A particle of charge q and mass m is projected from origin with an initial velocity v = ( v₀ 2 x + v₀ 2 y ) . There exists a uniform magnetic field B = B₀ z and a space varying ele 2026A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E ₁=E₀ x . If another electric field E ₂=2E₀( y + z ) is introduced to the s 2026 Full Electrostatics list All JEE Main PYQs