Question

Suppose a straight 1.00mm diameter copper wire could just "float"horizontally in air because of the force due to the Earth'smagnetic field (B), which is horizontal, perpendicular to the wire,and of magnitude 5.0x10^-5 T. What current would the wirecarry?

Answer 1

Let's examine the forces on a 1 meter piece of wire with radius 0.5e-3m

Copper has density of 8 960 kg/m^3. So a 1 meter long piece of wire would weigh

W = g . V . d
g is earth gravity
V is volume
d is density

W = 9.81m/s^2 x 3.14159 x (0.5e-3m)^2 x 1m x 8960 kg/m^3
W = 6.9e-2 N

The magnetic force is

F = B.I.L sin(A) where
B is magnetic field
I is current intensity
L is length
A is angle between mag field and current

So

I = F / (B.L.sin(A))
I = 6.9e-2 N / (0.5e-5T . 1m . sin(90)) = 1.38e4 A
I = 13 800 A