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NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice

A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R . One of the arcs AB of the ring subtends an angle θ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

Options

  1. Aproportional to ( 180 ° - θ )
  2. Binversely proportional to r
  3. Czero, only if ( θ = 180 ° )
  4. Dzero for all values of θ

Correct answer

D. zero for all values of θ

Step-by-step solution

For a current flowing into a circular arc, the magnetic induction at the centre is B = μ 0 i ⁡ 4 π  θ or B ∝ i ⁡ θ In the given problem, the total current is divided into two arcs i ⁡ ∝ 1 resistance of arc ∝ 1 length of arc ∝ 1 angle subtended at centre  θ or i θ = constant i.e., magnetic field at centre due to arc AB is equal and opposite to the magnetic field at centre due to arc ACB . Or the net magnetic field at the centre is zero

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