Question

A straight horizontal wire of mass 10 mg and length 1.0 m carries a current of 2.0 A. What minimum magnetic field B should be applied in the region, so that the magnetic force on the wire may balance its weight?

Answer 1

Given:
Mass of the wire, M = 10 mg = 10⁻⁵ Kg
Length of the wire, l = 1.0 m
Electric current flowing through wire, I = 2.0 A
As per the question, the weight of the wire should be balanced by the magnetic force acting on the wire.Also angle between the length of the wire and magnetic field is $90°$.
Thus, Mg = IlB, where
g is the acceleration due to gravity = 9.8 m/s²
B is the applied magnetic field
So,
$$\begin{gathered} B=\frac{M\mathrm{g}}{Il} \\ =\frac{{10}^{-5}\times 9.8}{2\times 1} \\ =4.9\times {10}^{-5}\mathrm{T} \end{gathered}$$