Question

A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5 m apart, in the negative Z-direction. A point P is at a perpendicular distance 3 m from the first wire and 4 m from the second. What will be magnitude of the magnetic field B at P?

पर्याय

• `5/8 (mu_0  "I")/pi`

• `5/24 (mu_0  "I")/pi`

• `7/24  mu_0  "I"`

• `25/64  mu_0  "I"`

Answer 1

`5/24 (mu_0  "I")/pi`

Explanation:

Magnetic field due to 1st wire,

`"B"_1 = (mu_0"I")/(2pi xx 3)      .....(because "R" = 3 "m")`

Magnetic field due to 2"d wire,

`"B"_2 = (mu_0"I")/(2pi xx 4)      .....(because "R" = 4 "m")`

Net magnetic field,

`"B" = sqrt ("B"_1^2 + "B"_2^2)`

`= (mu_0 "I")/(2pi) sqrt(1/9 + 1/16)`

`= (mu_0 "I")/(2pi) sqrt(25/144)`

`= (mu_0"I")/(2pi) xx 5/12`

` = (5 mu_0  "I")/(24 pi)`