Two point charges `q_(1)=2xx10^(-3) C` and `q_(2)=-3xx10^(-6) C` are separated by a distance `x = 10` cm. Find the magnitude and nature of the force between the two charges.

Answer

To solve the problem of finding the magnitude and nature of the force between two point charges \( q_1 \) and \( q_2 \), we will use Coulomb's Law. Here are the steps involved:

### Step 1: Identify the given values
We have:
- Charge \( q_1 = 2 \times 10^{-3} \, \text{C} \)
- Charge \( q_2 = -3 \times 10^{-6} \, \text{C} \)
- Distance \( r = 10 \, \text{cm} = 0.1 \, \text{m} \)

### Step 2: Write Coulomb's Law
Coulomb's Law states that the force \( F \) between two point charges is given by:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ F = 9 \times 10^9 \frac{|(2 \times 10^{-3})(-3 \times 10^{-6})|}{(0.1)^2} \]

### Step 4: Calculate the numerator
Calculate the product of the charges:
\[ |q_1 q_2| = |(2 \times 10^{-3})(-3 \times 10^{-6})| = 6 \times 10^{-9} \, \text{C}^2 \]

### Step 5: Calculate the denominator
Calculate \( r^2 \):
\[ r^2 = (0.1)^2 = 0.01 \, \text{m}^2 \]

### Step 6: Substitute back into the formula
Now substitute these values back into the force equation:
\[ F = 9 \times 10^9 \frac{6 \times 10^{-9}}{0.01} \]

### Step 7: Simplify the equation
This simplifies to:
\[ F = 9 \times 10^9 \times 6 \times 10^{-9} \times 100 \]
\[ F = 9 \times 6 \times 10^{9 - 9 + 2} = 54 \times 10^2 = 5400 \, \text{N} \]

### Step 8: Determine the nature of the force
Since \( q_1 \) is positive and \( q_2 \) is negative, the force is attractive. Therefore, the nature of the force is attractive.

### Final Answer
The magnitude of the force between the two charges is \( 5400 \, \text{N} \) and the nature of the force is attractive.

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