What current would be maintained in a circular coil of wire of 1000 turns and 10 cm in radius in order to just cancel the earth's magnetic field at a place where the horizontal component of Earth's magnetic field is `2 xx 10^(-4)T.`

Explanation

To solve the problem of finding the current that would be maintained in a circular coil of wire to cancel the Earth's magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the current \( I \) in a circular coil of wire with 1000 turns and a radius of 10 cm that will produce a magnetic field equal in magnitude but opposite in direction to the Earth's magnetic field, which has a horizontal component of \( B_E = 2 \times 10^{-4} \, \text{T} \).

2. **Formula for Magnetic Field of a Circular Coil**: The magnetic field \( B \) at the center of a circular coil is given by the formula:
\[
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