Two long, straight wires are parallel and 10 cm apart. One carries a current of 2.0 A, the other a current of 5.0 A. What is the magnitude and direction of the force per unit length exerted by the first wire on the second wire if the currents flow in the same direction?

and attractive(towards to each other)

Explanation:

We are given that

Distance between wires,d=10 cm=

We have to find the magnitude and direction of the force per unit length exerted by the first wire on the second wire if the currents flow in the same direction.

We know that magnetic force per unit length

Where

Using the formula

When the wires carrying current in same direction then the force between the wires attract to each other.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west