An electron having charge `'e'` and mass `'m'` is moving a uniform electric field `E`. Its acceleration will be

Options

A. `(e^(2))/(m)`
B. `(e E)/(m)`
C. `(eE^(2))/(m)`
D. `(mE)/e`

Explanation

To solve the problem of finding the acceleration of an electron moving in a uniform electric field \( E \), we can follow these steps:

### Step 1: Understand the forces acting on the electron
When a charged particle, such as an electron, is placed in an electric field, it experiences an electric force. The force \( F \) acting on the electron due to the electric field can be expressed as:
\[ F = eE \]
where:
- \( e \) is the charge of the electron (which is negative, but we will consider the magnitude for this calculation),
- \( E \) is the strength of the electric field.

### Step 2: Apply Newton's Second Law
According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration \( a \):
\[ F = ma \]
For our case, we can equate the force experienced by the electron to the mass times acceleration:
\[ eE = ma \]

### Step 3: Solve for acceleration
To find the acceleration \( a \), we can rearrange the equation from Step 2:
\[ a = \frac{F}{m} = \frac{eE}{m} \]
Thus, the acceleration of the electron in the uniform electric field \( E \) is given by:
\[ a = \frac{eE}{m} \]

### Final Answer
The acceleration of the electron is:
\[ \boxed{\frac{eE}{m}} \]

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