A short magnet oscillates in a vibration magnetometer with a time period of 0.10 s where the horizontal component of earth's magnetic field is `24 mu T` . An upward current of 18 A is established in the vertical wire placed 20 cm east of the magnet . Find the new time period.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
- The initial time period \( T_1 \) of the magnet is \( 0.10 \, \text{s} \).
- The horizontal component of Earth's magnetic field \( B_H \) is \( 24 \, \mu T \) (microtesla).
- A vertical wire carrying a current of \( 18 \, A \) is placed \( 20 \, cm \) (or \( 0.2 \, m \)) east of the magnet.

### Step 2: Calculate the magnetic field due to the current
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