Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
A circular loop of radius r carries a current i . How must a long, straight wire carrying a current 4i be positioned in the plane of the circle such that the magnetic field at the centre becomes zero?
Options
- AAt a distance of 4r from the centre, with its current direction opposite to that in the nearest part of the lo
- BAt a distance of 2r from the centre, with its current direction the same as that in the nearest part of the lo
- CAt a distance of 4r from the centre, with its current direction the same as that in the nearest part of the lo
- DAt a distance of 2r from the centre, with its current direction opposite to that in the nearest part of the lo
Correct answer
A. At a distance of 4r from the centre, with its current direction opposite to that in the nearest part of the lo
Step-by-step solution
The magnetic field at the centre of the circular loop due to its own current i is given by: B₁ = ₀ i 2r The magnetic field at the centre due to the long straight wire carrying current 4i at a distance d is: B₂ = ₀ (4i) 2 d For the net magnetic field at the centre to be zero, the magnitudes of the magnetic fields must be equal and their directions must be opposite. Equating the magnitudes: ₀ i 2r = ₀ (4i) 2 d d = 4r For the fields to be opposite at the centre, the straight wire must produce a magnetic field in the o