Q65 / 90 · JEE Main 2022 (26 Jul Shift 2) · Physics

Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be

  • A
    1:2
  • Correct answer
    B
    2:1
  • C
    1:1
  • D
    1:4

Solution

When two conductors are connected by a conducting wire, their potentials become equal. Therefore, VA=VB

The potential of a spherical conductor is given by, V=kQR

⇒kQARA=kQBRB

⇒Q∝R

Now the electric field near the surface of the conductor will be, E=kQR2

⇒EAEB=kQARA2kQBRB2=RBRA

⇒EAEB=105=21

Hence, the correct answer is option: 'B'.

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