Question

A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field `vec B = (0.4 mT) hat j + (0.6 mT) hat k` is switched on, in the region. The force acting on the segment is ______.

पर्याय

• `(2 hat j + 3 hat k)` mN

• `(-3 hat j + 2 hat k)` μN

• `(6 hat j + 4 hat k)` mN

• `(-4 hat j + 6 hat k)` μN

Answer 1

A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field `vec B = (0.4 mT) hat j + (0.6 mT) hat k` is switched on, in the region. The force acting on the segment is `bbunderline((-3 hat j + 2 hat k) mu N)`.

Explanation:

Given: I =  0.5 A,

l = 1 `hat i` cm = 10⁻² `hat i` m,

`vec B = (0.4 mT) hat j + (0.6 mT) hat k`

`vec F = I(vec l xx vec B)`

= `0.5 xx 10^-3 |(hat i, hat j, hat k), (10^-2, 0, 0), (0, 0.4, 0.6)|`

= `0.5 xx 10^-3 [-(0.6 xx 10^-2) hat j + (0.4 xx 10^-2) hat k]`

= `0.5 (-6 hat j + 4 hat k) mu N`

= `(-3 hat j + 2 hat k) mu N`