A steam of similar negatively charged particals enters an electrical field normal to the electric lines of force with a velocity of `3xx10^7 m//s`. The electric intensity is 1800 V/m . Then the specific charge value of in `C Kg^(-1)` is

Options

A. `2xx10^(10)`
B. `2xx10^(7)`
C. `2xx10^(11)`
D. `2xx10^(4)`

Explanation

To find the specific charge of the negatively charged particles, we need to follow these steps:

### Step 1: Understand the given parameters
- Velocity of particles, \( v = 3 \times 10^7 \, \text{m/s} \)
- Electric field intensity, \( E = 1800 \, \text{V/m} \)

### Step 2: Calculate the force acting on the charged particles
The force \( F \) acting on a charged particle in an electric field is given by:
\[ F = qE \]
where \( q \) is the charge of the particle.

### Step 3: Relate force to acceleration
Using Newton's second law, the force can also be expressed as:
\[ F = ma \]
where \( m \) is the mass of the particle and \( a \) is its acceleration. Therefore, we can equate the two expressions for force:
\[ qE = ma \]

### Step 4: Calculate the acceleration
From the equation above, we can express acceleration \( a \) as:
\[ a = \frac{qE}{m} \]

### Step 5: Calculate the time taken to travel a certain distance
Assuming the particles travel a distance \( d \) in the electric field, we can use the formula for distance:
\[ d = vt \]
Rearranging gives:
\[ t = \frac{d}{v} \]

### Step 6: Calculate the deflection in the electric field
The vertical deflection \( y \) of the particles in the electric field can be calculated using the formula:
\[ y = \frac{1}{2} a t^2 \]
Substituting \( a \) and \( t \):
\[ y = \frac{1}{2} \left(\frac{qE}{m}\right) \left(\frac{d}{v}\right)^2 \]

### Step 7: Rearranging for specific charge
The specific charge \( \frac{q}{m} \) can be expressed as:
\[ \frac{q}{m} = \frac{2y v^2}{E d^2} \]

### Step 8: Substitute known values
Assuming \( y = 2 \times 10^{-3} \, \text{m} \) (2 mm) and \( d \) is the distance traveled in the electric field, we can plug in the values to find \( \frac{q}{m} \).

### Step 9: Calculate specific charge
Using the values:
\[ \frac{q}{m} = \frac{2 \times (2 \times 10^{-3}) \times (3 \times 10^7)^2}{1800 \times d^2} \]
Assuming \( d \) is known or can be approximated, we can calculate \( \frac{q}{m} \).

### Final Calculation
Assuming \( d \) is also given or can be deduced from the context, we can compute the specific charge in \( C \, kg^{-1} \).