Question

A wire of length \(5\,mm\) carries a current of \(5A\) along the X-axis. Find the magnetic field at a point on the Y-axis at a distance \(1m\).

• A. \(1.0\times10^{-9}T\)
• B. \(2.5\times10^{-9}T\)
• C. \(5.0\times10^{-9}T\)
• D. \(1\times10^{-6}T\)

Hint:

For a short current element, \[ dB=\frac{\mu_0}{4\pi}\frac{Idl\sin\theta}{r^2} \] which is the differential form of Biot-Savart law.

Answer 1

The Correct Option is B

Using Biot-Savart law for a small current element, \[ dB= \frac{\mu_0}{4\pi} \frac{I\,dl\sin\theta}{r^2} \] Given \[ I=5A \] \[ dl=5\times10^{-3}m \] \[ r=1m \] \[ \theta=90^\circ \] Therefore, \[ B = 10^{-7} \times5 \times5\times10^{-3} \] \[ B=2.5\times10^{-9}T \] Final Answer: \[ \boxed{2.5\times10^{-9}T} \] Hence option \[ \boxed{(B)} \]