Question

Three circular concentric wires of radii a, 2a, and 3a are carrying currents 3I, 2I, and I respectively in the anticlockwise direction. The effective magnetic field at the common center is ____________.

Options

• `(13 mu_0  "I")/(6"a")`

• `(mu_0  "I")/"a"`

• `(7 mu_0  "I")/(6"a")`

• `(5 mu_0  "I")/(6"a")`

Answer 1

Three circular concentric wires of radii a, 2a, and 3a are carrying currents 3I, 2I, and I respectively in the anticlockwise direction. The effective magnetic field at the common center is `(13 mu_0  "I")/(6" a")`.

Explanation:

`"B"_1 = mu_0/(2"a") 3"I"`

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

`"B"_3 = (mu_0 "I")/(2(3"a"))`

`therefore  "B" = "B"_1 + "B"_2 + "B"_3`

`= (mu_0 "I")/(2"a") [3 + 2/2 + 1/3]`

`= (mu_0 "I")/(2"a") [3 + 1 + 1/3]`

`= (mu_0 "I")/(2"a") [13/3]`

`= (13 mu_0 "I")/(6"a")`