A straight 2.20 m wire carries a typical household current of 1.50 A (in one direction) at a location where the earth's magnetic field is 0.550 gauss from south to north.

Find the magnitude of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from west to east.

Question

A straight 2.20 m wire carries a typical household current of 1.50 A (in one direction) at a location where the earth's magnetic field is 0.550 gauss from south to north.

Find the magnitude of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from west to east.

anonymous · Answer

First, you need to get everything in SI - .550 gauss = 5.50E-5 T.
A current-varying wire with a magnetic field has a magnetic force acting on it equivalent to$$\vec F_B=-\int_C i \vec B \times d\vec s$$which, given  the symmetry, orthogonality, and simplicity of the problem, becomes the much more managable$$|\vec F_b|=iBl$$where i is current, B is the magnetic field vector, and l is the length of the wire.  I assume you can plug it in, right?

anonymous · Answer

1.815*10^-4