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. `-(3E)/(2)`
B. `-E`
C. `-(E)/(2)`
D. `-2E`

Explanation

To solve the problem, we need to determine the electric field at the location of the charge `-2Q` due to the charge `Q`. We will follow these steps:

### Step 1: Understand the setup
We have two point charges:
- Charge `Q` at point A
- Charge `-2Q` at point B

The distance between the two charges is `D`.

### Step 2: Calculate the electric field at the location of charge `Q`
The electric field `E` at the location of charge `Q` due to the charge `-2Q` can be expressed using Coulomb's law:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{-2Q}{D^2} \]
This electric field `E` is directed towards the charge `-2Q` since it is negative.

### Step 3: Calculate the electric field at the location of charge `-2Q`
Now, we need to find the electric field at the location of charge `-2Q` due to charge `Q`. The electric field `E'` at the location of charge `-2Q` can be expressed as:
\[ E' = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q}{D^2} \]
This electric field `E'` is directed away from the charge `Q` since it is positive.

### Step 4: Relate the two electric fields
From the previous steps, we have:
- Electric field at `Q`: \( E = \frac{-2Q}{4 \pi \epsilon_0 D^2} \)
- Electric field at `-2Q`: \( E' = \frac{Q}{4 \pi \epsilon_0 D^2} \)

### Step 5: Find the relationship between `E` and `E'`
To find the relationship between `E` and `E'`, we can express `E'` in terms of `E`:
\[ E' = -\frac{1}{2} E \]
This means that the electric field at the location of `-2Q` is half the magnitude of the electric field at `Q`, but in the opposite direction.

### Final Answer
Thus, the electric field at the location of `-2Q` is:
\[ E' = -\frac{E}{2} \]