Protons having kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field so that it just misses a plane target kept at a distance I in front of the accelerator. Find the magnetic field.

Explanation

To solve the problem, we need to find the magnetic field \( B \) that causes protons to bend in a way that they just miss a target placed at a distance \( l \) from the accelerator. Here is a step-by-step solution:

### Step 1: Understand the Motion of Protons in a Magnetic Field
When protons enter a magnetic field perpendicularly, they experience a magnetic force that causes them to move in a circular path. The radius \( r \) of this circular path can be expressed in terms of the mass \( m \), velocity \( v \), charge \( q \), and magnetic field \( B \).

### Step 2: Relate the Radius to the Distance \( l \)
Since the protons just miss the target at a distance \( l \), we can equate the radius of the circular path to \( l \):
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