Force on currents: A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod?

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Quizplus · Accepted Answer

The magnetic force ($F_B$) needed to cancel out the weight of the rod ($F_g$) can be found using the equation for the magnetic force on a current-carrying conductor: $F_B = I L B$, where $I$ is the current, $L$ is the length of the conductor, and $B$ is the magnetic field strength. The weight of the rod is given by $F_g = m g$, where $m$ is the mass of the rod and $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$). Setting $F_B = F_g$, we get $I L B = m g$. Solving for $I$, we have $I = \frac{m g}{L B}$. Substituting the given values ($m = 0.050 \, \text{kg}$, $g = 9.8 \, \text{m/s}^2$, $L = 1.0 \, \text{m}$, $B = 0.10 \, \text{T}$), we find $I = \frac{0.050 \times 9.8}{1.0 \times 0.10} = 4.9 \, \text{A}$.

Force on Currents: a Thin Copper Rod That Is 1