Consider the situation when an electric field E is present in a conductor. Acceleration a of the free electrons of the conductor due to this field is

Options

A. `a=(eE)/m`
B. `a=e/(Em)`
C. `a=E/(em)`
D. `a=(-eE)/m`

Answer

To find the acceleration \( a \) of the free electrons in a conductor when an electric field \( E \) is present, we can follow these steps:

### Step 1: Understand the Force on an Electron
When an electric field \( E \) is applied to a conductor, it exerts a force on the free electrons present in the conductor. The force \( F \) on an electron can be expressed using the equation:
\[ F = Q \cdot E \]
where \( Q \) is the charge of the electron. For an electron, the charge \( Q \) is equal to \( -e \) (where \( e \) is the elementary charge, approximately \( 1.6 \times 10^{-19} \) coulombs).

### Step 2: Substitute the Charge of the Electron
Substituting the charge of the electron into the force equation, we have:
\[ F = -e \cdot E \]
This indicates that the force acting on the electron is in the direction opposite to that of the electric field due to the negative charge of the electron.

### Step 3: Apply Newton's Second Law
According to Newton's second law, the force acting on an object is also equal to the mass of the object multiplied by its acceleration:
\[ F = m \cdot a \]
where \( m \) is the mass of the electron and \( a \) is its acceleration.

### Step 4: Set the Two Expressions for Force Equal
Now we can set the two expressions for force equal to each other:
\[ m \cdot a = -e \cdot E \]

### Step 5: Solve for Acceleration
To find the acceleration \( a \), we rearrange the equation:
\[ a = \frac{-e \cdot E}{m} \]
This shows that the acceleration of the free electrons is directly proportional to the electric field \( E \) and inversely proportional to the mass \( m \) of the electron.

### Final Expression
Thus, the acceleration \( a \) of the free electrons in the conductor due to the electric field \( E \) is given by:
\[ a = -\frac{e \cdot E}{m} \]