Question

Magnetic field \(|B|\) at a point \(P\) in the following network is:

• A. \(\frac{\mu_0 I}{4\pi R} \left(\frac{3}{2} \pi \right)\)
• B. \(\frac{\mu_0 I}{4\pi R} \left(\frac{3}{2} \pi + 2 \right)\)
• C. \(\frac{\mu_0 I}{4\pi R} \left(\frac{3}{2} \pi - 2 \right)\)
• D. \(\frac{3 \mu_0 I}{2 R}\)

Hint:

For calculating magnetic fields from current-carrying conductors, use the Biot-Savart law and consider the contributions from each section of the wire.

Answer 1

The Correct Option is A

The given circuit involves two current-carrying conductors forming a network with a point \(P\) located near them. The magnetic field at \(P\) due to each segment of the circuit can be calculated using Ampère's law and the Biot-Savart law. The total magnetic field at point \(P\) is a summation of the contributions from each segment. The correct expression for the magnetic field at \(P\) is given by: \[ |B| = \frac{\mu_0 I}{4\pi R} \left(\frac{3}{2} \pi \right) \]