Question

Two concentric circular coils of 'n' turns each are situated in the same plane. Their radii are 'a₁' and 'a₂' (a₂ > a₁) and they carry currents 'I₁' and 'I₂' respectively (I₁> I₂) in opposite direction. The magnetic field at the centre is ____________.

Options

• `(mu_0  "n")/2 [("I"_1 "a"_1 - "I"_2 "a"_2)/("a"_1 "a"_2)]`

• `(mu_0  "n")/(2  "I"_1 "I"_2) ["a"_1 - "a"_2]`

• `(mu_0  "n")/(2 "a"_1 "a"_2) [("I"_1 - "I"_2]`

• `(mu_0 "n")/2 [("I"_1 "a"_2 - "I"_2 "a"_1)/("a"_1 "a"_2)]`

Answer 1

Two concentric circular coils of 'n' turns each are situated in the same plane. Their radii are 'a₁' and 'a₂' (a₂ > a₁) and they carry currents 'I₁' and 'I₂' respectively (I₁> I₂) in opposite direction. The magnetic field at the centre is `(mu_0 "n")/2 [("I"_1 "a"_2 - "I"_2 "a"_1)/("a"_1 "a"_2)]`.

Explanation:

Magnetic fields due to the two coils are in opposite directions and are given by

`"B"_1 = (mu_0 "nI"_1)/(2"a"_1)   "and"   "B"_2 = (mu_0 "nI"_2)/(2"a"_2)`

`therefore "B" = "B"_1 - "B"_1`

`= (mu_0 "nI")/2 ["I"_1/"a"_1 - "I"_2/"a"_2]`

`= (mu_0 "nI")/2 [("I"_1 "a"_2 - "I"_2 "a"_1)/("a"_1 "a"_2)]`