Electromagnetism Question

In summary, the total force on a wire segment carrying a current of 1.8A from point a to point b in a uniform magnetic field of 1.2T acting in the z-direction is 0.0864i - 0.0648j. This is equal to the force on a straight wire segment from a to b. The right-hand rule and the formula F=BIL were used to determine the direction and magnitude of each force.
  • #1
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1. "A wire segment carries a current of 1.8A from a to b. There is a uniform magnetic field of 1.2T acting in the z-direction. Find the total force on the wire and show that the total force is the same as if the wire were a straight segment from a to b".

I've attached the diagram showing what the segment looks like and I've called the point between a and b, c.


2. Homework Equations : F=BIL

3. Would this be right?:
Fac = ILBcos90 = 0N (90° since the x-direction is orthogonal to z)
Fcb = ILBsin90 = ILB = 1.8 x 0.04 x 1.2 = 0.0864N (90° since the y-direction is orthogonal to z)
=> Facb = 0.0864N

Fab = ILBsinθ = ILBsin(arctan(4/3)) = 0.8ILB = 0.8 x 1.8 x 0.05 x 1.2 = 0.0864N

Therefore, Facb = Fab

Or is it just a coincidence that the two values come out to be the same? Because I don't really understand why it would be cos90 from a to c and sin90 from c to b =s
 

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  • #2
Welcome to PF :smile:

There are some problems with your derivation. For one, all currents (ac, cb, and ab) are perpendicular to the magnetic field. So use F=BIL to find each force, with no cos or sin factors. None of the three forces will be zero.

You'll also need to use the right-hand rule to figure out the direction of each force, and combine the ac & cb forces.
 
  • #3
Thanks for replying,
So, would this be right:
Fac = ILB = 0.0648N in the -ve y-direction so -0.0648j
Fcb = ILB = 0.0864N in the +ve x-direction so 0.0864i
=> Facb = 0.0864i - 0.0648j

Fab = ILB = 0.108N
The direction is sin(arctan(4/3))Fi - cos(arctan(4/3))Fj
= 0.0864i - 0.0648j

Not sure about the signs though because the right-hand rule really confuses me =s
 
Last edited:
  • #4
Looks good! The signs are correct too.
 
  • #5
Oh good :smile:
Thanks a lot.
 

1) What is electromagnetism?

Electromagnetism is a fundamental force of nature that describes the interaction between electrically charged particles. It is responsible for phenomena such as electricity, magnetism, and light.

2) How do electromagnets work?

Electromagnets work by using an electric current to create a magnetic field. When the current flows through a wire, it generates a magnetic field around the wire. By coiling the wire, the magnetic field is amplified, creating a strong electromagnet.

3) What are the applications of electromagnetism?

Electromagnetism has a wide range of applications in our daily lives. Some examples include electric motors, generators, telecommunication systems, MRI machines, and various electronic devices.

4) What is the relationship between electricity and magnetism?

Electricity and magnetism are closely related and are actually two different aspects of the same force, electromagnetism. An electric current creates a magnetic field, and a changing magnetic field can induce an electric current.

5) How does electromagnetism relate to light?

Light is an electromagnetic wave, which means it is a combination of electric and magnetic fields oscillating in a perpendicular direction. This connection between electricity and magnetism allows us to use electromagnetism to produce and detect light in various forms, including radio waves, microwaves, and visible light.

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