Question

A long straight wire of circular cross-section (radius \(a\)) carries a steady current \(I\). The current is uniformly distributed across this cross-section. The magnitude of the magnetic field produced at a point at a distance \(\dfrac{a}{2}\) from the axis of the wire will be

• A. Zero
• B. \(\dfrac{\mu_0 I}{2\pi a}\)
• C. \(\dfrac{\mu_0 I}{4\pi a}\)
• D. \(\dfrac{\mu_0 I}{6\pi a}\)

Hint:

For a point inside a wire carrying uniformly distributed current, \[ B=\frac{\mu_0 Ir}{2\pi a^2}, \] where \(r<a\). Substitute \(r=\dfrac{a}{2}\) directly to obtain \[ B=\frac{\mu_0 I}{4\pi a}. \]

Answer 1

The Correct Option is C