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IAT IISER2026PhysicsElectrostatics

Three infinite plane sheets which have uniform positive surface charge densities , and 2 , are arranged parallel to each other with a separation of d as shown in the figure. A spherical Gaussian surface S of radius d/2 has its center on the middle sheet. Which of the following statements regarding the electric flux _L through the left hemisphere and the electric flux _R through the right hemisphere of the Gaussian su

Options

  1. A_L = _R .
  2. B_L = 2 _R .
  3. C_L < _R .
  4. D_L > _R .

Correct answer

D. _L > _R .

Step-by-step solution

Let the middle sheet be located at x = 0 . Then the left sheet is at x = -d and the right sheet is at x = d . The electric field in the region between the left and middle sheets ( -d E_L = E_ left + E_ middle + E_ right E_L = 2 ₀ - 2 ₀ - 2 2 ₀ = - ₀ The electric field E_L is non-zero and points towards the left. Since the outward normal of the left hemisphere also points leftwards, the electric flux through the left hemisphere is positive ( _L > 0 ). The electric field in the region between the middle and right she

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