Homework help -- magnetic field from a wire causing compass deflection....

[Shozaba]

Homework Statement

A current 2A flows in a wire. Value of horizontal component of Earth magnetic field in the region is 2x10^-5T. Small compass placed 5cm due north of the wire. Calculate the angle through which the needle deflects due to the current flowing in the wire. Assume u0= 4pi x 10^-7 Hm^-1

Homework Equations

B=uI/2piR
F=BILsinx
Pythagoras a2+b2=c2

The Attempt at a Solution

Tried B=uI/2piR -> 2x10^-5=u2/2pi(0.05)
But that didn't make sense so I tried to solve for R instead and got R equal to 0.02 but didn't know what to do with R.
Then I tried using F=BILsinx and assumed sinx=90 assuming it was perpendicular but the question wants the angle through so I don't think F=BILsinx is relevant?

Please help thanks

 

[berkeman]

Homework Statement

A current 2A flows in a wire. Value of horizontal component of Earth magnetic field in the region is 2x10^-5T. Small compass placed 5cm due north of the wire. Calculate the angle through which the needle deflects due to the current flowing in the wire. Assume u0= 4pi x 10^-7 Hm^-1

Homework Equations

B=uI/2piR
F=BILsinx
Pythagoras a2+b2=c2

The Attempt at a Solution

Tried B=uI/2piR -> 2x10^-5=u2/2pi(0.05)
But that didn't make sense so I tried to solve for R instead and got R equal to 0.02 but didn't know what to do with R.
Then I tried using F=BILsinx and assumed sinx=90 assuming it was perpendicular but the question wants the angle through so I don't think F=BILsinx is relevant?

Please help thanks

Welcome to the PF.

It will help you to make a drawing of the setup. Have the wire coming out of the page toward you, with the current coming up at you. So the B-field circulates counter-clockwise around the wire, right? (by the Right Hand Rule).

Draw a vertical axis and a horizontal axis on your figure -- the vertical axis points up toward north, and the horizontal axis points to the right towards the east. The wire is coming up at you from the origin of those x-y axes.

Draw where the compass is. When there is no current in the wire, you are given what the Earth's B-field is, and it makes the compass point due north (at least in this simple problem). When the current is switched on, the B-fields from the Earth and from the wire add up vectorially, giving a new resultant B-field vector at the compass. This causes the compass needle to deflect one way or the other. Your task is to add up those two B-fields to see what how much the resultant B-field vector rotates compared to true north.

Have at it!

 

[Shozaba]

hi thanks for that i tried it and i added the two B-field vectors together, i just want to know what do i do with this and if my sketch is correct
thanks again
i got B-field for the wire= 2.55x10^-6= u0(2)/2pi(0.05)
added both B-fields together= 5.1x10^-11T

 

[berkeman]

earth magnetic field in the region is 2x10^-5T

i got B-field for the wire= 2.55x10^-6

How did you add those and get:

added both B-fields together= 5.1x10^-11T

Also, you need to add them vectorially. They do not point in the same direction...

As a tip, you might re-draw the diagram to more closely match what I suggested. It should be orthogonal x and y axes, with the wire coming out of the page vertically at the origin. Then the compass sits some distance up the y-axis, as described in the problem statement.

 

[Shozaba]

sorry i forgot to mention the wire is vertical, also this isn't homework its a question from a past paper. my physics tutor is stumped on it, he said that you if you add them vectorially then the B-fields move in the same direction. I am really finding this hard its only the second question in the paper. thanks