A particle of mass `2 xx 10^(-3)` kg, charge `4 xx 10^(-3)C` enters in an electric field of `5 V//m`, then its kinetic energy after 10 s is

Options

A. 0.1 J
B. 1 J
C. 10 J
D. 100 J

Answer

To solve the problem step by step, we will follow the physics principles related to electric fields, forces, acceleration, and kinetic energy.

### Step 1: Calculate the Force on the Particle
The force \( F \) experienced by a charged particle in an electric field is given by the formula:
\[ F = qE \]
where:
- \( q = 4 \times 10^{-3} \, \text{C} \) (charge of the particle)
- \( E = 5 \, \text{V/m} \) (electric field strength)

Substituting the values:
\[ F = (4 \times 10^{-3}) \times (5) = 2 \times 10^{-2} \, \text{N} \]

### Step 2: Calculate the Acceleration of the Particle
Using Newton's second law, the acceleration \( a \) can be calculated as:
\[ a = \frac{F}{m} \]
where:
- \( m = 2 \times 10^{-3} \, \text{kg} \) (mass of the particle)

Substituting the values:
\[ a = \frac{2 \times 10^{-2}}{2 \times 10^{-3}} = 10 \, \text{m/s}^2 \]

### Step 3: Calculate the Final Velocity after 10 seconds
Using the first equation of motion:
\[ v = u + at \]
Assuming the initial velocity \( u = 0 \) (the particle starts from rest), and substituting \( a = 10 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \):
\[ v = 0 + (10)(10) = 100 \, \text{m/s} \]

### Step 4: Calculate the Kinetic Energy
The kinetic energy \( KE \) of the particle is given by:
\[ KE = \frac{1}{2} mv^2 \]
Substituting \( m = 2 \times 10^{-3} \, \text{kg} \) and \( v = 100 \, \text{m/s} \):
\[ KE = \frac{1}{2} \times (2 \times 10^{-3}) \times (100)^2 \]
\[ KE = \frac{1}{2} \times (2 \times 10^{-3}) \times (10^4) = \frac{1}{2} \times 20 = 10 \, \text{J} \]

### Final Answer
The kinetic energy of the particle after 10 seconds is \( \boxed{10 \, \text{J}} \).

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