Question

Find the magnetic field at \( P \) due to the arrangement shown:

• A. \( \dfrac{H_0}{2 \sqrt{2}} \left( 1 + \dfrac{1}{\sqrt{2}} \right) \)
• B. \( \dfrac{H_0}{2 \sqrt{2}} \left( 1 - \dfrac{1}{\sqrt{2}} \right) \)
• C. \( \dfrac{H_0}{2 \sqrt{2}} \)
• D. \( \dfrac{H_0}{2 \sqrt{2}} \left( 1 + \dfrac{1}{\sqrt{3}} \right) \)

Hint:

The magnetic field due to a current-carrying conductor can be calculated using the Biot-Savart law, which depends on the geometry and distance from the point of interest.

Answer 1

The Correct Option is A

Step 1: The magnetic field at point \( P \) is calculated using the Biot-Savart law. The field at \( P \) due to the current in the conductor is dependent on the distance from the wire and the angle of the current relative to \( P \).
Step 2: Based on the configuration and the current, the magnetic field at point \( P \) is given by: \[ B = \dfrac{H_0}{2 \sqrt{2}} \left( 1 + \dfrac{1}{\sqrt{2}} \right). \]
Final Answer: \[ \boxed{\dfrac{H_0}{2 \sqrt{2}} \left( 1 + \dfrac{1}{\sqrt{2}} \right)} \]