Question

A 1 cm straight segment of a conductor carrying 1 A current in x direction lies symmetrically at origin of Cartesian coordinate system. The magnetic field due to this segment at point (1m, 1m, 0) is ______.

Options

• `1.0 xx 10^-9 hat k T`

• `-1.0 xx 10^-9 hat k T`

• `5.0/sqrt2 xx 10^-10 hat k T`

• `-5.0/sqrt2 xx 10^-10 hat k T`

Answer 1

A 1 cm straight segment of a conductor carrying 1 A current in x direction lies symmetrically at origin of Cartesian coordinate system. The magnetic field due to this segment at point (1m, 1m, 0) is `bbunderline(-5.0/sqrt2 xx 10^-10 hat k T)`.

Explanation:

Given: I = 1 A

dl = 0.01 m

Observation point: P(1, 1, 0)

r = `sqrt(1^2 + 1^2)`

= `sqrt 2`

Using Biot-Savart law:

dB = `(mu_0)/(4 pi) (Idl xx r)/r^3`

For a small element at x = 0,

dl × r = `dx hat k`

Magnetic field (B) = `(mu_0)/(4 pi) * (dx hat k)/r^3`

= `(10^-7 xx 0.01)/(sqrt 2)^3 hat k`

= `10^-9/(2 sqrt 2) hat k`

= `(-5.02)/sqrt 2 xx 10^-10 hat k T`