# Electromagnetism Question

#### ryanwilk

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. Relevant 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

#### Attachments

• 142.5 KB Views: 168

#### Redbelly98

Staff Emeritus
Homework Helper
Welcome to PF 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.

#### ryanwilk

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:

#### Redbelly98

Staff Emeritus
Homework Helper
Looks good! The signs are correct too.

#### ryanwilk

Oh good Thanks a lot.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving