# Problem: A 9.0-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.33 Ohms. Pulling the wire with a force of 1.2 N causes 3.9 W of power to be dissipated in the circuit. What is the speed of the wire when pulled with 1.2 N?

###### FREE Expert Solution

Power in circuits:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{V}}{\mathbf{i}}{\mathbf{=}}{{\mathbf{i}}}^{{\mathbf{2}}}{\mathbf{R}}{\mathbf{=}}\frac{{\mathbf{V}}^{\mathbf{2}}}{\mathbf{R}}}$

Also,

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{F}}{\mathbf{v}}}$

Force:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{i}}{\mathbf{L}}{\mathbf{B}}}$

Given that 3.9 W of power is to be dissipated, we'll consider the equation:

P = V2/R

V = sqrt(PR) = sqrt[(3.9)(0.33)] = 1.134V

87% (13 ratings) ###### Problem Details

A 9.0-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.33 Ohms. Pulling the wire with a force of 1.2 N causes 3.9 W of power to be dissipated in the circuit. What is the speed of the wire when pulled with 1.2 N?