The electric force on a charge `q_1` due to `q_2` is `(4hati-3hatj)N`. What is the force on `q_2` due to `q_1`

Explanation

To find the force on charge \( q_2 \) due to charge \( q_1 \), we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that the force exerted by \( q_1 \) on \( q_2 \) will be equal in magnitude but opposite in direction to the force exerted by \( q_2 \) on \( q_1 \).

Given:
- The electric force on charge \( q_1 \) due to \( q_2 \) is \( \vec{F}_{12} = (4 \hat{i} - 3 \hat{j}) \, \text{N} \).

To find the force on \( q_2 \) due to \( q_1 \), denoted as \( \vec{F}_{21} \), we can apply the following steps:

### Step 1: Identify the given force
The force on \( q_1 \) due to \( q_2 \) is given as:
\[ \vec{F}_{12} = 4 \hat{i} - 3 \hat{j} \]

### Step 2: Apply Newton's third law
According to Newton's third law:
\[ \vec{F}_{21} = -\vec{F}_{12} \]

### Step 3: Calculate the force on \( q_2 \)
Substituting the value of \( \vec{F}_{12} \):
\[ \vec{F}_{21} = -(4 \hat{i} - 3 \hat{j}) = -4 \hat{i} + 3 \hat{j} \]

### Final Answer
Thus, the force on charge \( q_2 \) due to charge \( q_1 \) is:
\[ \vec{F}_{21} = -4 \hat{i} + 3 \hat{j} \, \text{N} \]