What will be the change in electric field, if the charge on an object in halved ?

Options

A. Electric field will be doubled
B. Electric field will also become half
C. Electric field will remain same
D. None of them

Answer

To find the change in the electric field when the charge on an object is halved, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Electric Field Formula**:
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. **Identify the Initial Electric Field**:
Let's denote the initial charge as \( Q \). The electric field at a distance \( r \) from this charge is:
\[ E = \frac{kQ}{r^2} \]

3. **Halve the Charge**:
If the charge is halved, the new charge \( Q' \) becomes:
\[ Q' = \frac{Q}{2} \]

4. **Calculate the New Electric Field**:
Now, substituting \( Q' \) into the electric field formula, we get the new electric field \( E' \):
\[ E' = \frac{kQ'}{r^2} = \frac{k \left(\frac{Q}{2}\right)}{r^2} = \frac{kQ}{2r^2} \]

5. **Relate the New Electric Field to the Initial Electric Field**:
We can express \( E' \) in terms of the initial electric field \( E \):
\[ E' = \frac{1}{2} \cdot \frac{kQ}{r^2} = \frac{E}{2} \]

6. **Conclusion**:
Therefore, if the charge on an object is halved, the electric field at a certain distance from that object will also be halved.

### Final Answer:
The electric field will become half if the charge on an object is halved.

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