JEE Main202427 Jan 2024Morning ShiftPhysicsElectrostaticsActual
A thin metallic wire having cross sectional area of 10 - 4 m 2 is used to make a ring of radius 30 cm . A positive charge of 2 π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is _______ N ; provided that the ring does not get deformed (neglect the influence of gravity). (Given, 1 4 π ϵ 0 = 9 × 10 9 SI units)
Correct answer
0
Step-by-step solution
The linear charge density of the ring is given by λ = Q 2 π R . . . 1 With reference to the above diagram, for the equilibrium condition of the ring, it can be written that 2 T s i n d θ 2 = 1 4 π ε 0 q 0 R 2 · λ R d θ ⇒ T = 1 4 π ε 0 q 0 Q R 2 × 2 π [As for very small angles sin d θ 2 = d θ 2 ] = 9 × 10 9 2 π × 30 × 10 - 12 ( 0 . 30 ) 2 × 2 π = 9 × 10 - 3 × 30 9 × 10 - 2 = 3 N