A wire with length 3.5 m and mass 0.03 kg is aligned horizontally and connected by conducting loops to two vertical frictionless metal rods. The rod is oriented in the East-West direction. What is the magnitude of the current that has to be run through the wire so that it hovers in place without sliding up or down? You may ignore magnetic forces caused by the vertical wires. Earth's magnetic field: 0.00005 Tesla or 0.5 gauss. Earth's gravity: 9.8 N/kg

Current flowing in the wire is 1680 A

Explanation:

It is given length of wire l = 3.5 m

Mass of the wire m = 0.03 kg

Magnetic field B = 0.00005 Tesla

Acceleration due to gravity

Mg force acting on the wire will be equal to Lorentz force acting on the wire.

Therefore

Therefore current flowing in the wire is 1680 A

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm