# Homework Help: A Wire and a Compass

1. Mar 6, 2008

### cse63146

1. The problem statement, all variables and given/known data

You are looking straight down on a magnetic compass that is lying flat on a table. A wire is stretched horizontally under the table, parallel to and a short distance below the compass needle. The wire is then connected to a battery so that a current flows through the wire. This current causes the north pole of the compass needle to deflect to the left. The questions that follow ask you to compare the effects of different actions on this initial deflection.

Part A: If the wire is lowered farther from the compass, how does the new angle of deflection of the north pole of the compass needle compare to its initial deflection?

i) It is Smaller
ii) It is unchanged
iii) It is bigger

Part B: With the wire back at its initial location, you connect a second identical battery in series with the first one. When you close the switch, how does the new angle of deflection of the north pole of the compass needle compare to its initial deflection?

i) It is Smaller
ii) It is unchanged
iii) It is bigger

2. Relevant equations

B = $$\frac{(\mu_0)qvsin\vartheta}{4(\pi)r^2}$$

3. The attempt at a solution

I got the answer for part A (it is smaller) since the distance between the wire and the compass increases, the magnetic field produced by the wire weakens. Therefore, the north pole of the compass needle will deflect away from its original direction (determined by the magnetic field of the earth) by a smaller angle.

For Part B I believe the answer would be "It is bigger" since v = 2v (since it's in series), which would increase the magnetic field and thus produced a bigger angle.

Am I right?