A straight horizontal wire carrying a current of 2.0 ext A has a mass of 10 ext mg and a length of 1.0 ext m . Determine the minimum magnetic field B that must be applied in the region in order for the magnetic force on the wire to balance its weight.

Step-by-step solution

For the magnetic force to balance the weight of the wire, the magnetic force must act upwards and its magnitude must be equal to the gravitational force. The magnetic force on a current-carrying wire is given by F_ m = I L B . For the minimum magnetic field, = 90^ , so = 1 . Equating the magnetic force to the weight of the wire: I L B = m g Given: I = 2.0 A m = 10 mg = 10 10⁻⁶ kg = 10⁻⁵ kg L = 1.0 m g = 9.8 m/s ² Substituting the values: 2.0 1.0 B = 10⁻⁵ 9.8 B = 9.8 10⁻⁵ 2.0 B = 4.9 10⁻⁵ T