Question

In the given figure, the magnetic field at ‘O’.

• A. \frac{3}{4} \frac{\mu_o I}{r} + \frac{\mu_o I}{4 \pi r}
• B. \frac{3}{10} \frac{\mu_o I}{r} - \frac{\mu_o I}{4 \pi r}
• C. \frac{3}{8} \frac{\mu_o I}{r} + \frac{\mu_o I}{4 \pi r}
• D. \frac{3}{8} \frac{\mu_o I}{r} - \frac{\mu_o I}{4 \pi r}

Answer 1

The Correct Option is C

In the given problem, the magnetic field at point O is due to the two different segments of the current-carrying wire. We apply the Biot-Savart law to calculate the magnetic field contributions.
1. For the straight segment of the wire (along the horizontal direction): The magnetic field at point O due to this segment is given by the formula: \[ B_{\text{straight}} = \frac{\mu_0 I}{4 \pi r} \]
2. For the curved segment of the wire (in the circular loop): The magnetic field at point O due to this loop is given by the formula: \[ B_{\text{loop}} = \frac{3 \mu_0 I}{8 r} \] Thus, the total magnetic field at point O is the sum of the two contributions: \[ B_{\text{total}} = B_{\text{straight}} + B_{\text{loop}} = \frac{3 \mu_0 I}{8 r} + \frac{3 \mu_0 I}{4 \pi} \] Therefore, the correct answer is (C).