Question

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre '0' of the semicircle by three sections together is (μ₀ = permiability of free space) ______.

विकल्प

• \[\frac{\mu_0\mathrm{I}}{4\mathrm{R}}\]

• \[\frac{\mu_0\mathrm{I}}{2\mathrm{R}}\]

• \[\frac{\mu_0\mathrm{I}}{4π\mathrm{R}}\]

• \[\frac{\mu_0\mathrm{I}}{2π\mathrm{R}}\]

Answer 1

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre '0' of the semicircle by three sections together is (μ₀ = permiability of free space) \[\frac{\mu_0\mathrm{I}}{4\mathrm{R}}\].

Explanation:

The two straight sections contribute zero magnetic field at O because their current elements point directly toward the centre, making the cross product \[\overrightarrow {dl⃗}\] × \[\hat r\] = 0, so only the semicircular arc contributes B = \[\frac{\mu_0\mathrm{I}}{4\mathrm{R}}\].