Question

A 2.1 m long straight horizontal wire carrying a current of 5.1 A along the +x-direction is in a region of uniform magnetic field, B. If the mass of this wire is 0.2 kg, find the magnitude and direction of the magnetic field necessary to have this wire "float" in the Earth's gravitational field. (Assume the force due to gravity is in the −y-direction.)

Answer 1

Explanation:

It is given that,

Length of the wire, L = 2.1 m

Current, I = 5.1 A

Mass of the wire, m = 0.2 kg

Let B is the magnitude of the magnetic field necessary to have this wire "float" in the Earth's gravitational field such that,

$F_g=F_m$

$mg=ILB$

$B=\dfrac{mg}{IL}$

$B=\dfrac{0.2\times 9.8}{5.1\times 2.1}$

B = 0.18 T

The direction of magnetic field is given by Fleming's left hand rule. Here, the magnetic field is in +x direction.