Question

Hi, can I have some help with this problem? Step by Step explanations would be very helpful!! Thanks

A wire having a linear mass density of 1.00 g/cm is placed on a horizontal surface that has a coefficient of kinetic friction of 0.200. The wire carries a current of 1.50 A toward the east and slides horizontally to the north at constant velocity. What are the magnitude and the direction of the smallest magnetic field that enables the wire to move in this fashion?

Answer 1

The wire is experiencing a force in the north direction .The force experienced by a current carrying conductor placed in a magnetic field is given as
F = B i l
The direction of the current and the direction of magnetic field is perpendicular , so we dropped the cross product
Friction acts opposite to the direction of movement
The magnitude of friction is f = $\mu$ k x N
Where   $\mu$ k is the coefficient of the kinetic friction and N is the normal force
To find the minimum magnetic field we equate these two forces
B i l =    $\mu$ k x m x g
B =    $\mu$ k x m x g / i l
$\mu$ k = 0.200 , linear mass density m / l = 1 g /cm³  , i = 1.5 A ,g = 9.8 m /s²
B = 0.2 x 1000 x 9.8 / 1.5 = 1306.6 T
b) The direction of the magnetic field should be into the surface