Question

In the figure shown, the magnetic field induction as the point \( O \) will be

• A. \( \frac{\mu_0 I}{2r} \)
• B. \( \frac{\mu_0 I}{4r} \)
• C. \( \frac{\mu_0 I}{r} \)
• D. \( \frac{\mu_0 I}{3r} \)

Hint:

For a straight conductor carrying current, the magnetic field is inversely proportional to the distance from the conductor.

Answer 1

The Correct Option is A

Using Ampere's law and the magnetic field equation for a straight conductor, we calculate the magnetic field induction at the point \( O \). The formula for the magnetic field due to a current in a straight conductor is \( B = \frac{\mu_0 I}{2 \pi r} \). Since the point is along the perpendicular bisector of the conductor, the induction at point \( O \) is half of that.

Step 2: Conclusion.
The magnetic field induction at point \( O \) is \( \frac{\mu_0 I}{2r} \), corresponding to option (a).