A small compass is held horizontally and the centre of its needle is at the distance of 0.280 m directly north of the long wire that is perpendicular to the earth’s surface as in FIGURE 1. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the earth’s magnetic field at the location. The component is parallel to the earth’s surface. When the current in the wire is 25.0 A, the needle points 230 east of north.

Question

A small compass is held horizontally and the centre of its needle is at the distance of 0.280 m directly north of the long wire that is perpendicular to the earth’s surface as in FIGURE 1. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the earth’s magnetic field at the location. The component is parallel to the earth’s surface. When the current in the wire is 25.0 A, the needle points 230 east of north.

i) What is the possible diagram for the above condition?
ii) What is the magnitude of the horizontal component of the earth’s magnetic field at
the location of the compass?
iii) Explain what happen when current is increased
iv) Explain what happen when the current is reversed

Answer 1

i) To visualize the given condition, you can draw a diagram with the long wire placed perpendicular to the ground (similar to figure 1 mentioned in the question). Place a small compass horizontally to the north of the wire, with its center 0.280 m away from the wire. The compass needle should be pointing due north when there is no current in the wire and should point 230° east of north when the current in the wire is 25.0 A.

ii) To determine the magnitude of the horizontal component of the Earth's magnetic field at the location of the compass, we can use the information provided. When there is no current in the wire, the compass needle points due north, indicating that the Earth's magnetic field is aligned with the horizontal component, parallel to the surface. Let's consider the angle between the horizontal component of the Earth's magnetic field and due north as θ.

In this case, since the needle points due north, the angle θ is zero degrees. Therefore, the magnitude of the horizontal component of the Earth's magnetic field at the location of the compass can be assumed to be the same as the strength of the magnetic field due to the Earth.

iii) When the current in the wire is increased, the magnetic field produced around the wire also increases. This additional magnetic field interacts with the Earth's magnetic field and causes the compass needle to deviate from its initial north direction. The needle now points 230° east of north, indicating that the combined magnetic field pulls the needle towards the east.

The angle between the horizontal component of the Earth's magnetic field and the combined magnetic field (including the Earth's and the wire's magnetic fields) is now 230°. This means that the horizontal component of the Earth's magnetic field is not strong enough to counterbalance the combined magnetic field, causing the needle to deviate.

iv) When the current in the wire is reversed, the direction of the magnetic field around the wire changes. This reversed magnetic field interacts with the Earth's magnetic field, resulting in the compass needle pointing in the opposite direction.

If the wire's magnetic field is now pointing west, the magnetic field vector sum (the vector sum of the Earth's and wire's magnetic fields) will be the opposite of the previous scenario. Therefore, the compass needle will now point in the opposite direction, 230° west of north.

By reversing the current in the wire, the magnetic fields produced will also reverse, affecting the interaction with the Earth's magnetic field and thus changing the direction of the compass needle.