The photograph below shows a compass, with the red end of the compass pointing toward the north, inside a coil. Notice that Dan is about to connect a wire to the second contact of the coil so that about ten amperes of current will flow in the coil. The direction of the (positive) current in the coil is shown by the arrow on the coil. If it matters, the coil contains 10 turns of wire, and is about 7cm in radius.
When Dan connects the coil, it might cause the needle to deflect in a different direction, if the field is strong. On the other hand, if the magnetic field of the coil is a different type of field from that of the earth, perhaps nothing will happen. Or maybe the needle will just deflect slightly from where it is with no current in the coil.
When Dan connects the coil, what will happen?
- (a) The compass needle will point in the upward direction in the picture.
- (b) The compass needle will point in the downward direction in the picture.
- (c) The compass needle will point to the left in the picture.
- (d) The compass needle will point to the right in the picture.
- (e) The compass needle will remain where it is after the coil is connected.
- (f) The compass needle will deflect only slightly from where it is before the coil is connected (Specify which direction.)
Enough information has been given above so that a simple calculation can be made, if it is actually appropriate.
After July 18th, 2014, click Read More for the answer.
The answer is (b): the compass needle will point in the downward direction in the picture, as seen in an mpeg video by clicking your mouse on the photograph below.
Using the right hand rule, the red end of the coil will point in the direction of the field, which will be top-to-bottom in the picture. The magnetic field of the coil is considerably larger than that of the component of the earth's field in the north direction, so it will be the dominant magnetic field when the current is on.
Using the Biot-Savart law, the axial magnetic field of the 10-turn coil with radius of 7 cm carrying 10 amperes of current can be calculated:
and is approximately 10 gauss, about a factor of 10 greater than the magnetic field of the earth (about 1 gauss). Therefore, the compass needle will move to align itself with the magnetic field of the coil rather than that of the earth.