A positive charge and a negative charge are initially at rest. If same electric field is applied on them.

Options

A. both have acclerated motions in the direction of the field
B. both have retarded motions in the direction of the field
C. positive charge has accelerated motion in the direction of the field and negative charge has also accelerated motion but in a direction opposite to that of the field
D. Positive charge has accelerated motion in a direction opposite to that of the field and negative charge has also accelerated motion but in the direction of the field.

Answer

To solve the problem, we need to analyze the behavior of a positive charge and a negative charge when they are placed in the same electric field. Here’s the step-by-step solution:

### Step 1: Understand the Force on a Charge in an Electric Field
The force \( \mathbf{F} \) acting on a charge \( q \) in an electric field \( \mathbf{E} \) is given by the equation:
\[ \mathbf{F} = q \mathbf{E} \]

### Step 2: Analyze the Positive Charge
For a positive charge \( q \):
- The force \( \mathbf{F}_{+} \) acting on it will be in the same direction as the electric field.
- Therefore, if the electric field \( \mathbf{E} \) is directed to the right, the positive charge will also move to the right.

### Step 3: Analyze the Negative Charge
For a negative charge \( -q \):
- The force \( \mathbf{F}_{-} \) acting on it will be in the opposite direction to the electric field.
- Thus, if the electric field \( \mathbf{E} \) is directed to the right, the negative charge will move to the left.

### Step 4: Conclusion
- The positive charge accelerates in the direction of the electric field.
- The negative charge accelerates in the opposite direction of the electric field.

### Final Statement
In summary, when the same electric field is applied:
- The positive charge accelerates in the direction of the field.
- The negative charge accelerates in the opposite direction of the field.