A rough inclined plane inclined at angle `37°` with horizontal, has a metallic wire of length 20cm with its length `bot` to length, of inclined plane `( μ = 0.1)` When a current of i is passing through the wire and a magnetic field is applied normal to the plane upwards, the wire starts moving up with uniform velocity for B = 0.5T. Then find the magnitude of current i, (mass of the wire=50g)

Explanation

To solve the problem, we need to analyze the forces acting on the metallic wire on the inclined plane and apply the principles of physics to find the magnitude of the current \( i \).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Wire:**
- The weight of the wire \( W = mg \) acts downwards, where \( m = 50 \, \text{g} = 0.05 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \).
- The weight can be resolved into two components:
- Perpendicular to the incline: \( W_{\perp} = mg \cos \theta \)
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