A circular loop of radius r carries a current i. where should a long , straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?

Explanation

To solve the problem of where to place a long straight wire carrying a current of \(4i\) in the plane of a circular loop of radius \(r\ carrying a current \(i\) such that the magnetic field at the center of the loop becomes zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Magnetic Fields**:
- The magnetic field at the center of a circular loop carrying current \(i\) is given by the formula:
\[
B_{\text{loop}} = \frac{\mu_0 I}{2r}
...