If a charge particle (q) inters into the magnetic field at origin with velocity `v_(0)hat(i)`, then find the maximum possible positive x co-ordinate of particle if mag- netic field is given as
`B=B_(0)x(-hatk)xgt0`
`=0xlt0`

Explanation

To solve the problem, we need to analyze the motion of a charged particle in a magnetic field. The magnetic field is given as \( \mathbf{B} = B_0 x (-\hat{k}) \) for \( x > 0 \) and \( \mathbf{B} = 0 \) for \( x < 0 \). The particle enters the magnetic field at the origin with an initial velocity \( \mathbf{v} = v_0 \hat{i} \).

### Step-by-Step Solution:

1. **Identify the Force on the Particle**:
The force acting on a charged particle moving in a magnetic field is given by the Lorentz force equation:
\[
\mathbf{F} = q (\mathbf{v} \times \mathbf{B})
...