B →R graph. The mag. field B at a distance r from a long straight wire carrying a current varies

step 1 In this problem, the graph can be drawn something like this. Just look at it carefully. Here in

B →R graph. The mag. field B at a distance r from a long...

Key Concepts

Magnetic Field of a Current-Carrying Conductor

This concept deals with the phenomenon by which a steady electric current produces a magnetic field in the space around it. In the case of a long straight wire, the magnetic field lines form concentric circles around the wire, and the field's magnitude decreases as the distance from the wire increases.

Inverse Dependence of Magnetic Field on Distance

For a long straight current-carrying wire, the magnitude of the magnetic field is inversely proportional to the distance from the wire. This means that as you move further away from the wire, the magnetic field decreases in strength following a 1/r relationship, which is reflected in the corresponding B versus r graph.

Ampere's Law

Ampere’s Law is a fundamental principle in electromagnetism that relates the integrated magnetic field around a closed loop to the electric current passing through the loop. This law provides the theoretical basis for deriving the 1/r dependence of the magnetic field around a long straight conductor.

Biot–Savart Law

The Biot–Savart Law quantitatively describes the magnetic field generated by a small segment of current-carrying conductor. It is used to calculate the magnetic field for various current distributions, including the derivation of the magnetic field’s inverse relationship with distance in the case of a long straight wire.

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