In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is , however, not constant but increases uniformly along the positive z-direction. At the rate of `10^(5)NC^(-1)m^(-1)` . What are the force and torque experienced by system having a total dipole moment equal to `10^(-7)`Cm in the negative z-direction?

Explanation

To solve the problem, we need to calculate the force and torque experienced by a dipole in a non-uniform electric field. Let's go through the steps systematically.

### Step 1: Understand the Electric Field Variation
The electric field \( E \) is directed along the positive z-direction and increases uniformly at a rate of \( 10^5 \, \text{N/C/m} \). This means that the electric field at a distance \( z \) from the origin can be expressed as:
\[ E(z) = E_0 + \left(10^5 \, \text{N/C/m}\right) \cdot z \]
where \( E_0 \) is the electric field at \( z = 0 \).
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