Two points charges q and -2q are placed some distance d apart. If the electric field at the location of q is E, that at the location of -2q is

Options

A. `-E/2`
B. `-2E`
C. `E/2`
D. `-4E`

Answer

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

### Step-by-Step Solution:

1. **Identify the Charges and Their Positions**:
- We have two point charges: \( q \) (positive charge) and \( -2q \) (negative charge).
- They are placed a distance \( d \) apart.

2. **Electric Field at Charge \( q \)**:
- The electric field \( E \) at the location of charge \( q \) is due to the charge \( -2q \).
- The electric field \( E \) created by a point charge is given by the formula:
\[ E = \frac{k \cdot |Q|}{r^2} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge creating the field, and \( r \) is the distance from the charge to the point where the field is being calculated.

3. **Calculate the Electric Field at Charge \( -2q \)**:
- Now, we need to find the electric field at the location of charge \( -2q \) due to charge \( q \).
- The distance from \( q \) to \( -2q \) is \( d \).
- The electric field \( E' \) at the location of \( -2q \) due to charge \( q \) is:
\[ E' = \frac{k \cdot |q|}{d^2} \]

4. **Relate the Electric Fields**:
- From the problem, we know that the electric field at the location of \( q \) is \( E \).
- We can express \( E \) in terms of \( q \) and \( -2q \):
\[ E = \frac{k \cdot |(-2q)|}{d^2} = \frac{2kq}{d^2} \]
- Now, we can relate \( E' \) to \( E \):
\[ E' = \frac{k \cdot |q|}{d^2} \]
- Notice that \( E' \) is half of \( E \):
\[ E' = \frac{1}{2} \cdot \frac{2kq}{d^2} = \frac{E}{2} \]

5. **Conclusion**:
- The electric field at the location of charge \( -2q \) is:
\[ E' = \frac{E}{2} \]

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