The point charges `Q` and `-2Q` are placed at some distance apart. If the electirc field at the location of `Q` is `E`, the electric field at the location of `-2Q` will be

Options

A. (a) 3 E
B. (b) `E//2`
C. (c) E
D. (d) None of these

Answer

To solve the problem, we need to analyze the electric fields created by the point charges \( Q \) and \( -2Q \) at their respective locations.

### Step-by-Step Solution:

1. **Understanding Electric Fields**:
The electric field \( E \) due to a point charge \( Q \) at a distance \( r \) is given by the formula:
\[ E = \frac{kQ}{r^2} \]
where \( k \) is Coulomb's constant.

2. **Electric Field at the Location of Charge \( Q \)**:
- The electric field at the location of charge \( Q \) (due to charge \( -2Q \)) can be calculated as:
\[ E = \frac{k(-2Q)}{r^2} = -\frac{2kQ}{r^2} \]
However, since the problem states that the electric field at the location of \( Q \) is \( E \), we can denote:
\[ E = -\frac{2kQ}{r^2} \]

3. **Electric Field at the Location of Charge \( -2Q \)**:
- The electric field at the location of charge \( -2Q \) (due to charge \( Q \)) is:
\[ E' = \frac{kQ}{r^2} \]

4. **Relating the Electric Fields**:
- From the previous step, we have:
\[ E' = \frac{kQ}{r^2} \]
- Since we know that \( E = -\frac{2kQ}{r^2} \), we can express \( kQ/r^2 \) in terms of \( E \):
\[ kQ = -\frac{E \cdot r^2}{2} \]
- Substituting this back into the equation for \( E' \):
\[ E' = \frac{-\frac{E \cdot r^2}{2}}{r^2} = -\frac{E}{2} \]

5. **Final Result**:
- Therefore, the electric field at the location of charge \( -2Q \) is:
\[ E' = -\frac{E}{2} \]

### Conclusion:
The electric field at the location of charge \( -2Q \) is \( -\frac{E}{2} \).