A short bar magnet oscillates in VMM with a frequency of 10Hz. If a downward current of 15A is established in a long thin vertical wire placed 20 cm west of the magnet, its frequency was found to be 5Hz. If a TG containing 500 turns with radius of each turn `4pi` cm is used at that place & a current of 10mA is allowed to pass through it. Find the deflection of magnetic needle in the TG

Explanation

To solve the problem step by step, we will first analyze the given information and then apply the relevant formulas to find the deflection of the magnetic needle in the tangent galvanometer (TG).

### Step 1: Understand the Given Information
- Frequency of the bar magnet oscillating (f1) = 10 Hz
- Frequency with downward current (f2) = 5 Hz
- Current in the vertical wire (I) = 15 A
- Distance from the wire to the magnet (d) = 20 cm = 0.2 m
- Number of turns in the TG (N) = 500
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