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?
A) 1.2 A
B) 2.5 A
C) 4.9 A
D) 7.6 A
E) 9.8 A

Question

Quizplus · Accepted Answer

The magnetic force ($F_m$) needed to cancel the weight of the rod ($F_g$) can be calculated using the formula $F_m = BIL$, where $B$ is the magnetic field strength, $I$ is the current, and $L$ is the length of the rod. The weight of the rod is given by $F_g = mg$, where $m$ is the mass of the rod and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Setting $F_m = F_g$, we get $BIL = mg$. Solving for $I$, we find $I = \frac{mg}{BL}$. Substituting the given values ($m = 0.050 \, \text{kg}$, $B = 0.10 \, \text{T}$, $L = 1.0 \, \text{m}$, and $g = 9.8 \, \text{m/s}^2$), we get $I = \frac{0.050 \times 9.8}{0.10 \times 1.0} = 4.9 \, \text{A}$.

A Thin Copper Rod That Is 1