Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
A wire of total length 2 r carrying a current i is bent to form a regular polygon of n sides. Determine the magnetic field B at the centre of this polygon.
Options
- A₀ i n ( n ) ( n ) 2 ^2 r
- B₀ i n^2 ( n ) ( n ) 2 ^2 r
- C₀ i n^2 ( 2 n ) ( 2 n ) 4 ^2 r
- D₀ i n^2 ( n ) ( n ) 2 ^2 r
Correct answer
B. ₀ i n^2 ( n ) ( n ) 2 ^2 r
Step-by-step solution
Total length of the wire is 2 r . The polygon has n sides, so the length of each side is a = 2 r n . The perpendicular distance from the centre to any side is d = a 2 ( n ) = r n ( n ) . The magnetic field at the centre due to one side of the polygon is given by the formula for a finite straight wire: B₁ = ₀ i 4 d [ ( n ) + ( n ) ] Substituting the value of d : B₁ = ₀ i 4 ( r n ( n ) ) [ 2 ( n ) ] B₁ = ₀ i n ( n ) ( n ) 2 ^2 r Since the polygon has n identical sides and the magnetic field due to each side is in the