Two point charges `Q` and `-3Q` are placed at some distance apart. If the electric field at the location of `Q` is `E` then at the locality of `-3Q`, it is

Options

A. `-E`
B. `E//3`
C. `-3E`
D. `-E//3`

Explanation

To solve the problem, we need to find the electric field at the location of the charge `-3Q` when the electric field at the location of charge `Q` is given as `E`.

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have two point charges: `Q` and `-3Q`. These charges create electric fields at each other's locations. The electric field at the location of charge `Q` due to charge `-3Q` is given as `E`.

2. **Electric Field Due to a Point Charge**:
The electric field \( E \) due to a point charge \( Q \) at a distance \( r \) is given by the formula:
\[ E = \frac{k \cdot |Q|}{r^2} \]
where \( k \) is Coulomb's constant.

3. **Electric Field at Charge `Q`**:
The electric field \( E \) at the location of charge `Q` due to charge `-3Q` can be expressed as:
\[ E = \frac{k \cdot |-3Q|}{r^2} = \frac{3kQ}{r^2} \]
Here, \( r \) is the distance between the charges.

4. **Electric Field at Charge `-3Q`**:
Now, we need to find the electric field \( E' \) at the location of charge `-3Q` due to charge `Q`. Using the same formula:
\[ E' = \frac{k \cdot |Q|}{r'^2} \]
where \( r' \) is the distance from charge `Q` to charge `-3Q`. Since the distance between the two charges is the same, we can use the same \( r \) for simplicity.

5. **Relating the Electric Fields**:
We know from the principle of superposition that the force on charge `Q` due to `-3Q` is equal to the force on charge `-3Q` due to `Q`. Therefore, we can set up the relationship:
\[ Q \cdot E = (-3Q) \cdot E' \]
This implies:
\[ E' = -\frac{E}{3} \]

6. **Magnitude of Electric Field**:
The magnitude of the electric field at the location of charge `-3Q` is:
\[ |E'| = \frac{E}{3} \]
The negative sign indicates that the direction of the electric field at `-3Q` is opposite to that at `Q`.

### Final Answer:
Thus, the electric field at the locality of `-3Q` is:
\[ E' = -\frac{E}{3} \]