Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
Determine the magnetic field B at the centre of a rectangular loop having length l and width b , carrying a current i .
Options
- A4 ₀ i l^2 + b^2 l b
- B₀ i l^2 + b^2 l b
- C2 ₀ i l^2 + b^2 l b
- D₀ i l^2 + b^2 2 l b
Correct answer
C. 2 ₀ i l^2 + b^2 l b
Step-by-step solution
The magnetic field at the centre of the rectangular loop is the sum of the magnetic fields produced by its four sides. The magnetic field due to a finite straight wire of length L at a perpendicular distance d from its centre is given by: B' = ₀ i 4 d ( ₁ + ₂) For the two sides of length l , the perpendicular distance to the centre is d = b 2 . The angles are ₁ = ₂ = l l^2 + b^2 . The magnetic field due to these two sides is: B₁ = 2 ₀ i 4 ( b 2 ) ( 2l l^2 + b^2 ) = 2 ₀ i l b l^2 + b^2 For the two sides of length b