A gold rod of length `l` is accelerated in the horizontal direction with an accleration `a_(0)`. The rod is held between two perfactly insulating clamps. Calculate the electric field set up in the rod. Take the mass of electron as `m`.

Options

A. (a) `E = (ma_(0))/(e)`
B. (b) `E = ma_(0)l`
C. ( c) zero
D. ( d) none of these

Explanation

To solve the problem of calculating the electric field set up in a gold rod of length `l` that is accelerated horizontally with an acceleration `a_0`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Rod**:
The rod is being accelerated horizontally with an acceleration `a_0`. According to Newton's second law, the force acting on the rod can be expressed as:
\[ F = m \cdot a_0 \]
where `m` is the mass of the rod.

2. **Understand the Effect of Acceleration on Charges**:
The acceleration of the rod causes the free electrons within the rod to experience a force. This force will cause a separation of charges, leading to the creation of an electric field within the rod.

3. **Relate Electric Force to Electric Field**:
The electric force acting on an electron due to the electric field `E` can be expressed as:
\[ F_e = e \cdot E \]
where `e` is the charge of an electron.

4. **Set Up the Equation**:
Since the rod is accelerating, the force due to the acceleration must equal the electric force acting on the electrons. Therefore, we can equate the two forces:
\[ m \cdot a_0 = e \cdot E \]

5. **Solve for the Electric Field `E`**:
Rearranging the equation to solve for the electric field `E`, we get:
\[ E = \frac{m \cdot a_0}{e} \]

### Final Expression:
Thus, the electric field set up in the rod is given by:
\[ E = \frac{m \cdot a_0}{e} \]