A charged particle enters a magnetic field at right angles to the field. The field exists for a length equal to `1.5` times the radius of circular path of particle. The particle will be deviated from its path by

Options

A. `90^(@)`
B. `sin^(-1)(2//3)`
C. `30^(@)`
D. `180^(@)`

Explanation

To solve the problem, we need to analyze the motion of a charged particle entering a magnetic field at right angles. Here's a step-by-step solution:

### Step 1: Understand the scenario
A charged particle enters a magnetic field perpendicularly, which means it experiences a magnetic force that causes it to move in a circular path. The radius of this circular path is denoted as \( r \).

**Hint:** Remember that the force on a charged particle in a magnetic field is given by the Lorentz force, which causes circular motion when the particle enters at right angles.

### Step 2: Determine the length of the magnetic field
According to the problem, the length of the magnetic field \( L \) is given as \( 1.5 \) times the radius of the circular path:
\[ L = 1.5 \times r \]

**Hint:** Identify the relationship between the length of the magnetic field and the radius of the circular path to understand how far the particle will travel in the field.

### Step 3: Analyze the circular motion
When the particle enters the magnetic field, it will begin to move in a circular path with radius \( r \). The time it takes for the particle to complete a full circle is determined by its speed and the radius.

**Hint:** Recall that the particle will continue in a circular path until it exits the magnetic field.

### Step 4: Determine the angle of deviation
Since the length of the magnetic field \( L \) is \( 1.5r \), the particle will not complete a full circular path. Instead, it will travel through the magnetic field and exit after covering a distance of \( 1.5r \).

The particle will complete \( \frac{1.5r}{2\pi r} = \frac{1.5}{2\pi} \) of a full circle, which corresponds to an angle of:
\[ \theta = \frac{1.5}{2\pi} \times 360^\circ = \frac{540^\circ}{2\pi} \approx 86.6^\circ \]

However, since the particle is entering at right angles and the field length is more than the radius, it will deviate in the opposite direction after exiting. Thus, the total deviation will be:
\[ 180^\circ \]

**Hint:** Consider how the particle's path changes when it exits the magnetic field and how this relates to the angle of deviation.

### Step 5: Conclusion
The deviation of the particle from its original path after exiting the magnetic field is \( 180^\circ \).

**Final Answer:** The particle will be deviated from its path by \( 180^\circ \).