Magnitude and direction of the total force on the wire

[negat1ve]

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!

 

[Hannisch]

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!

 

[negat1ve]

Sorry, it was a 63 degree angle I had.

 

[negat1ve]

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!

 

[negat1ve]

ok, i solved this, thanks!

 

[meme123]

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