A certain length of insulated wire can be bent to form either a single circular loop (case I) or a double loop of smaller radius (case II). When the same steady current is passed through the wire, the ratio of the magnetic field at the cent

Question

A certain length of insulated wire can be bent to form either a single circular loop (case I) or a double loop of smaller radius (case II). When the same steady current is passed through the wire, the ratio of the magnetic field at the centre in (case I) to that in (case II) is

Quantrex Academy · Accepted Answer

Correct answer: D. 1 / 4

Magnetic field at the centre due to current carrying circular loop having N turns is given as B= ₀ N I 2 r If l be the length of wire, then for the first case, aligned 2 r₁ &=l r₁ &= l 2 Magnetic field, B₁ &= ₀ 1 I 2 r₁ = ₀ I 2 l / 2 B₁ &= ₀ I l ...(i) aligned For the second case, 2 2 r₂=l r₂= l 4 B₂= ₀ 2 I 2 r₂ = 2 ₀ I 2 l 4 B₂= 4 ₀ I l =4 B₁ [from . Eq .( i ) ] B₁ B₂ = 1 4

A certain length of insulated wire can be bent to form either a single circular loop (case I) or a double loop of smaller radius (case II). When the same steady current is passed through the wire, the ratio of the magnetic field at the centre in (case I) to that in (case II) is

Options

Correct answer

Step-by-step solution

More from Magnetic Effects of Current