A wire with a linear mass density of 1.17 g/cm moves at a constant speed on a horizontal surface and the coefficient of kinetic friction between the wire and the surface is 0.250. If the wire carries a current of 1.24 A westward and moves horizontally to the south, determine the magnitude and direction of the smallest magnetic field that can accomplish this.

The value is

The direction is into the surface

Explanation:

From the question we are told that

   The mass density is  

   The coefficient of kinetic friction is  

   The current the wire carries is  

Generally the magnetic force acting on the wire is mathematically represented as

Here   is the frictional  force which is mathematically represented as

While  is the magnetic force which is mathematically represented as

Here is the angle between the direction of the force and that of the current

So

So

=>  

=>  

=>  

Apply the right hand curling rule , the thumb pointing towards that direction of the current we see that the direction of the magnetic field is into the surface as shown on the first uploaded image

answer would be letter choice (a),   a ball resting on a shelf. would be another example of potential energy   >   stored energy > not moving.

a ball spinning on a finger   >   kinetic energy > moving energy

a ball rolling on the ground   >   kinetic energy   > moving energy

a   ball flying through the air   > kinetic energy   >   moving energy

hope that                                         : )