Question

Two toroids 1 and 2 have total number of turns 400 and 200 respectively with average radii 40 cm and 20 cm respectively. If they carry same current I, the ratio of the magnetic fields along the two loops is, ____________.

Options

• 1 : 2

• 1 : 1

• 4 : 1

• 2 : 1

Answer 1

Two toroids 1 and 2 have total number of turns 400 and 200 respectively with average radii 40 cm and 20 cm respectively. If they carry same current I, the ratio of the magnetic fields along the two loops is, 1 : 1.

Explanation:

Magnetic field inside a toroid is given by,

`"B" = mu_0 "nI" = (mu_0  "NI")/(2pi  "R")`

∴ For first toroid,

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

For second toroid,

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

`therefore "B"_1/"B"_2 = "N"_1/"R"_1 xx "R"_2/"N"_2`

`= 400/0.4 xx 0.2/200`

`= 1 : 1`