A particle of mass 12g and charge `80 mu C` moves through a uniform magnetic field, in a region where the free - fall acceleration is `-9.8 hat(j) m//s^(2)`. The velocity of the particle is a constant `20 hat(i) km//s`, which is perpendicular to the magnetic field. What then is the magnetic field ?

Explanation

To solve the problem, we need to find the magnetic field \( \mathbf{B} \) acting on a charged particle moving through it. Here's a step-by-step breakdown of the solution:

### Step 1: Identify the given values
- Mass of the particle, \( m = 12 \, \text{g} = 12 \times 10^{-3} \, \text{kg} \)
- Charge of the particle, \( q = 80 \, \mu \text{C} = 80 \times 10^{-6} \, \text{C} \)
- Velocity of the particle, \( \mathbf{v} = 20 \, \text{km/s} = 20 \times 10^{3} \, \text{m/s} \) in the direction of \( \hat{i} \)
- Acceleration due to gravity, \( \mathbf{g} = -9.8 \, \hat{j} \, \text{m/s}^2 \)

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