The magnetic field produced by a current-carrying straight wire at a point outside the wire depends

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Question

This question was previously asked in

NDA 01/2022: General Ability Test Previous Year Paper (Held On 10 April 2022)

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inversely on the distance from it
directly on the distance from it
inversely at short distances and directly at large distances from it
directly on the distance (at short distances) and inversely on the distance (at long distances) from it

Answer 1

CONCEPT:

Magnetic Field is a field in space around a magnet or moving charged particle where another magnet or moving charged particle experiences a Force.
- A moving charged particle produces a magnetic field.
- A current-carrying wire contains moving electrons into it, hence generate a magnetic field around it.
Magnetic Field generated around the current (I) carrying conductor at a distance R from the wire:

\(\Rightarrow \vec B = \frac{\mu_0\vec I}{2\pi R}\)

Where \(\frac { \mu_0}{2\pi}\) has a constant value, I is current, and R is the distance of the point from the wire.

EXPLANATION:

Magnetic field intensity,

\(\Rightarrow B = \frac{μ_0I}{2π r}\)

\(⇒ B ∝ \frac{1}{r}\)

From the above formula, it is clear that the magnetic field generated is inversely proportional to the distance from the current-carrying wire.