Electric field of a system of charges does not depend on

Options

A. position of charges forming the system
B. distance of point (at which field is being observed) from the charges forming system
C. value of test charge used to find out the field
D. separation of charges forming the syst

Answer

To solve the question, "Electric field of a system of charges does not depend on," we need to analyze the factors that influence the electric field created by a system of charges.

### Step-by-Step Solution:

1. **Understanding Electric Field**:
The electric field (E) at a point in space due to a charge (or a system of charges) is defined as the force (F) experienced by a small positive test charge (q₀) placed at that point, divided by the magnitude of the test charge:
\[ E = \frac{F}{q₀} \]

2. **Coulomb's Law**:
According to Coulomb's law, the force between two point charges \( q_A \) and \( q_B \) separated by a distance \( r \) is given by:
\[ F = \frac{1}{4 \pi \epsilon_0} \frac{q_A q_B}{r^2} \]

3. **Electric Field Calculation**:
When calculating the electric field due to a charge \( q \) at a distance \( r \), we can express it as:
\[ E = \frac{F}{q₀} = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \]
Notice that in this expression, the test charge \( q₀ \) cancels out.

4. **Dependence on Charge Position**:
The electric field does depend on the position of the source charges (the charges creating the field) because the distance \( r \) from the charge to the point where the field is being measured is crucial.

5. **Dependence on Distance**:
The electric field does depend on the distance from the charge; as the distance increases, the electric field strength decreases.

6. **Dependence on Test Charge**:
The electric field is independent of the value of the test charge \( q₀ \). This is because the electric field is a property of the source charges and their configuration, not of the test charge used to measure it.

7. **Conclusion**:
Therefore, the electric field of a system of charges does not depend on the value of the test charge used to find out the field.

### Final Answer:
The electric field of a system of charges does not depend on the value of the test charge used to find out the field.