Magnitude and direction of the total force on the wire

In summary, the conversation discusses a problem involving a stiff wire bent at a right angle, with one section lying along the z-axis and the other along the line y=2x in the xy plane. A current of 20A flows through the wire, and it is placed in a uniform magnetic field given by B=(0.318i)T. The goal is to find the magnitude and direction of the total force on the wire. The conversation includes attempts at solving the problem, with one person calculating the force on each section and adding them, while another person suggests using vector addition. Eventually, the problem is solved and the answer is found to be F=2.13N and the force lies at an angle of 41.
  • #1
negat1ve
24
0

Homework Statement


A stiff wire 50 cm (0.5 m) long is bent at a right angle in the middle. One section loes along the z axis and the other is along the line y=2x in the xy plane. A current of 20A flows in the wire -down the z-axis and out the line in the xy plane. The wire passes through a uniform magnetic field given by B=(0.318i)T determine the magnitude and direction of the total force on the wire.

Homework Equations


F = I l B sin(theta)
F = I lxB

The Attempt at a Solution



I tried solving the problem by finding the force on each section and adding them.

Along the z-axis the angle with the mag field would be 90, so I get the force to be 1.59N

In the xy-plane, the section lies on the line y=2x. So it makes a 27 degree angle with the mag field. So I get the force to be 0.72N.

After adding them I get the force F = 1.59 + 0.72 = 2.31N

Now I have an answer key that says the force F=2.13N and lies 41.8 degrees below negative y-axis.

How do I get these results? What am I doing wrong? Thanks for your time!
 
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  • #2


Well, you're dealing with forces - i.e. vectors. Vector addition isn't quite as simple as you've made it..

Ah, and one other thing - I don't quite agree with you on your angle!
 
  • #3


Sorry, it was a 63 degree angle I had.
 
  • #4


sorry, can anyone walk me through this problem or hint at some steps i need to do this. why can't i simply use the equation f= I l b sin(theta) using the angles i found the wire to be.

Is when the mag field is given as B=(.318i)T mean that it is only in the x direction? Thats what i am thinking but I am confusing myself now. Thanks guys!
 
  • #5


ok, i solved this, thanks!
 
  • #6


I have a similar method. I tried it the exact way that you tried. Did you use any other equations?
 

FAQ: Magnitude and direction of the total force on the wire

1. What is the magnitude of the total force on the wire?

The magnitude of the total force on the wire is the overall strength or intensity of the force acting on the wire. It is typically measured in Newtons (N) and can be calculated by multiplying the force applied to the wire by the cosine of the angle between the force and the wire.

2. How is the direction of the total force on the wire determined?

The direction of the total force on the wire is determined by the vector sum of all the individual forces acting on the wire. This can be done using vector addition, where the magnitude and direction of each force are taken into account to determine the resultant force.

3. What factors affect the magnitude and direction of the total force on the wire?

The magnitude and direction of the total force on the wire can be affected by several factors, such as the strength and direction of each individual force, the angle between the forces, and the properties of the wire itself (e.g. length, material, etc.). Other external factors like friction and air resistance can also impact the total force on the wire.

4. How can the total force on the wire be calculated?

The total force on the wire can be calculated by adding all the individual forces acting on the wire together. This can be done using vector addition, where the magnitude and direction of each force are taken into account. Alternatively, if the forces acting on the wire are known to be in equilibrium (i.e. balanced), then the total force would be equal to zero.

5. Why is it important to consider both magnitude and direction in determining the total force on the wire?

Magnitude and direction are both crucial components in determining the total force on the wire. The magnitude of the force gives us information about the strength or intensity of the force, while the direction tells us where the force is acting. Both factors are necessary in order to accurately understand and predict the motion and behavior of the wire under the influence of the total force.

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