## Mastering Physics Solutions: A Wire and a Compass

A Wire and a Compass

Part A = It is smaller
Part B = It is larger

Solutions Below:

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 I 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?

This should be somewhat intuitive. We normally think about compasses responding to the Earth’s magnetic field, not a wire’s, but the farther from the magnetic field you are, the less that the needle is going to move.

It is smaller

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?

Since there will be more electricity, and therefore a greater magnetic field, the angle will have to increase.

It is larger

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