A horizontal wire is oriented along an east-west line, and a...

Name: Problem 9, Chapter 14: The Physics of Everyday Phenomena: A Conceptual Introduction to Physics
Uploaded: 2021-09-19T16:18:37-08:00
Duration: 3 min 35 s
Channel: Vishal Gupta
Description: A horizontal wire is oriented along an east-west line, and a compass is placed above it. Will the needle of the compass deflect when a current flows through the wire from east to west, and if so, in what direction? Explain.

A horizontal wire is oriented along an east-west line, and a compass is placed above it. Will the needle of the compass deflect when a current flows through the wire from east to west, and if so, in what direction? Explain.

Key Concepts

Magnetic Field from a Current-Carrying Conductor

A current flowing through a conductor produces a magnetic field that circulates around the wire. The magnitude and direction of the field at any point in space can be determined using principles such as Ampere’s law or the Biot–Savart law. This field forms concentric circles around the conductor, with its direction given by a well-established rule.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the magnetic field generated by a current. By pointing the thumb of the right hand in the direction of current flow, the curl of the fingers indicates the orientation of the magnetic field lines around the wire. This concept is crucial in analyzing how a current’s magnetic field interacts with other magnetic elements.

Compass Needle Behavior in Magnetic Fields

A compass needle aligns itself with the net magnetic field acting on it. When an external magnetic field is introduced, such as that produced by a nearby current-carrying conductor, the needle experiences a torque and deflects to align along the resultant field vector. The deflection depends on the vector sum of the Earth’s magnetic field and any additional magnetic fields present.

Superposition of Magnetic Fields

The magnetic field at any point in space is the vector sum of all individual magnetic fields acting at that point. In scenarios where a compass is affected by both the Earth’s magnetic field and an additional field from a current-carrying wire, the overall direction that the compass needle points is determined by combining these fields. This principle explains how the additional magnetic field from the wire can cause a measurable deflection in the compass needle.

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