Question

The magnetic field developed due to current carrying coil at its centre is 'B'. If the new coil of two turns is prepared from the above coil and same current is passed, then the magnetic field at the centre of the new coil will be ____________.

Options

• 2B

• `"B"/2`

• `"B"/4`

• 4B

Answer 1

The magnetic field developed due to current carrying coil at its centre is 'B'. If the new coil of two turns is prepared from the above coil and same current is passed, then the magnetic field at the centre of the new coil will be 4B.

Explanation:

`"B"_1 = (mu_0"nI")/(2"R"_1) = (mu_0"I")/(2"R"_1)`

`varphi = 2pi"R"_1`

`= 2pi"R"_2 (2)`

`= 4pi "R"_2`

`therefore 2 pi"R"_1 = 4 pi"R"_2`

`"R"_1/"R"_2 = 2`

`"B"_2 = (mu_0 2"I")/(2"R"_2)`

`"B"_1/"B"_2 = (mu_0"I")/(2"R"_1) xx (2"R"_2)/(mu 2"I") = 1/2 xx 1/2`

`"B"_2 = 4"B"_1`