Question

The ratio of the magnetic field at the centre of a current-carrying circular wire and the magnetic field at the centre of a semi-circular coil made from the same length of wire will be ______.

Options

• 2: 1

• 4: 1

• 1: 2

• 1: 4

Answer 1

The ratio of the magnetic field at the centre of a current-carrying circular wire and the magnetic field at the centre of a semi-circular coil made from the same length of wire will be 4: 1.

Explanation:

The magnetic field at the centre of the circular coil,

(L = 2`pi"r"_1`)

`"B"_"circular" = = µ_0/ (4pi) (2pi"i")/"r"_1 = µ_0/(4pi) (4pi^2"i")/"L"` and

Magnetic field at the centre of semi-circular coil, (L = `pi`2 )

`"B"_"semi-circular" = = µ_0/ (4pi) (pi"i")/"r"_2 = µ_0/(4pi) (4pi^2"i")/"L"`

∴ `"B"_"circular"/"B"_"semi-circular"` = 4