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

Three concentric conducting spherical shells A, B and C have radii a, b and c respectively (a < b < c) and carry charges q₁, q₂ and q₃ respectively. If the potential of the innermost shell A is equal to the potential of the outermost shell C , then which of the following relations is correct?

Options

  1. Aq₁ ( 1 a + 1 c ) + q₂ ( 1 b + 1 c ) = 0
  2. Bq₁ a = q₁+q₂ c
  3. Cq₁ ( 1 a - 1 c ) + q₂ ( 1 b - 1 c ) = 0
  4. Dq₁ + q₂ = 0

Correct answer

C. q₁ ( 1 a - 1 c ) + q₂ ( 1 b - 1 c ) = 0

Step-by-step solution

Let k = 1 4 ₀ . The potential of the innermost shell A is the sum of potentials due to its own charge and the charges on shells B and C . Since A is inside B and C , their contributions are constant and equal to their surface potentials: V_A = k q₁ a + k q₂ b + k q₃ c The potential of the outermost shell C is due to its own charge and the charges on A and B . Since C is outside A and B , they act as point charges at the centre: V_C = k q₁ c + k q₂ c + k q₃ c Given V_A = V_C : k ( q₁ a + q₂ b + q₃ c ) = k ( q₁ c + q

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