A10.0-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 0.350ohms . pulling the wire at a steady speed of 4.0m/s causes 4.20w of power to be dissipated in the circuit. part a: how big is the pulling force? part b: what is the strength of the magnetic field?

A) 1.05 N

The power dissipated in the circuit can be written as the product between the pulling force and the speed of the wire:

where

P = 4.20 W is the power

F is the magnitude of the pulling force

v = 4.0 m/s is the speed of the wire

Solving the equation for F, we find

B) 3.03 T

The electromotive force induced in the circuit is:

(1)

where

B is the strength of the magnetic field

v = 4.0 m/s is the speed of the wire

L = 10.0 cm = 0.10 m is the length of the wire

We also know that the power dissipated is

(2)

where

is the resistance of the wire

Subsituting (1) into (2), we get

And solving it for B, we find the strength of the magnetic field:

e/c, where e is its total energy