Magnetic field problem with two wires -

[Annette123]

Homework Statement

I was given this question on a "practice final" and I have no idea how to approach it whatsoever...any help (particularly if you could walk me through it...physics isn't my forte...!) would be greatly appreciated!

"Two long straight wires are oriented perpendicular to the page as shown in the diagram. The current in one wire is I1 = 3.0 A pointing into the page, and the current in the other wire is I2 = 4.0 A pointing out of the page. What is the magnitude of the net magnetic field at point P? Refer to the previous question. What is the direction of the net magnetic field at point P? Give your answer in degrees, measured CLOCKWISE from the positive x direction."

(Please see figure attached)

Thank you so, so much in advance for your help!

Homework Equations

I honestly don't know (sorry!)

The Attempt at a Solution

I don't know where to begin (again, many apologies)!

 

[TSny]

I don't know where to begin (again, many apologies)!

Hello.
You can begin by telling us something about your understanding of the properties of the magnetic field of a long straight wire.

Could you answer the question if only one current (I₁, say) was present?

 

[Annette123]

I believe so...that would be using the formula

F=ILBsin(theta)

correct? =/

 

[TSny]

I believe so...that would be using the formula

F=ILBsin(theta)

correct? =/

No, that equation is for calculating magnetic force acting on a current. You have a very different problem. You want to find the magnetic field at a point of space produced by two currents.

I am sure you have covered the properties of the magnetic field produced by currents. You need to review that topic.

 

[Arkavo]

no that's a force use the biot savart law

 

[Annette123]

Ok, so I think I have a slightly better idea as to how I'm supposed to be approaching this...I have the equation

B=(mu X I)/(2 X pi X r), and I have plugged in values for both of the wires so that one of the magnetic fields = 1.2X10^-5 T (the wire with a current of 3 A which is only 0.05m from the point) and the other magnetic field = 1.13137...X10^-5 T (the wire with a current of 4 A which is ~0.0707...m from the point, as I figured out using Pythagorean theorem)...I presume I'm supposed to somehow put them together using vector addition...? Then I suppose it should be the right-hand rule to figure out direction, but there are two wires...how should that work?

 

[TSny]

Good. Yes, you need to use the right hand rule to figure out the direction of each of the two magnetic fields that you calculated. Then add the two magnetic field vectors using vector addition.

Are you having trouble using the right hand rule to determine the direction of the field from each current, or are you having trouble adding the two vectors?

 

[Annette123]

Good. Yes, you need to use the right hand rule to figure out the direction of each of the two magnetic fields that you calculated. Then add the two magnetic field vectors using vector addition.

Are you having trouble using the right hand rule to determine the direction of the field from each current, or are you having trouble adding the two vectors?

To be honest both (I know it's a little silly...but physics REALLY isn't my forte) - could you please walk me through it?

 

[TSny]

Take a look at the pictures on this page and this page and see if that helps.