Net charge within an imaginary cube drawn in a uniform electric field is always zero. Is this statement true or false?

Explanation

To determine whether the statement "Net charge within an imaginary cube drawn in a uniform electric field is always zero" is true or false, we can analyze the situation step by step.

### Step 1: Understanding the Concept of Electric Field
In a uniform electric field, the electric field lines are parallel and evenly spaced. This means that the strength of the electric field is constant throughout the region.

**Hint:** Remember that a uniform electric field has consistent field lines that do not vary in strength or direction.

### Step 2: Visualizing the Cube in the Electric Field
When we place an imaginary cube in this uniform electric field, we can visualize how the electric field lines interact with the surfaces of the cube.

**Hint:** Draw a diagram of the cube and the electric field lines to see how they enter and exit the cube.

### Step 3: Analyzing Electric Flux
The electric flux (Φ) through a surface is defined as the product of the electric field (E) and the area (A) of the surface through which the field lines pass, taking into account the angle (θ) between the field lines and the normal to the surface. For a uniform electric field, if we consider the cube, the flux entering one face of the cube will be equal to the flux exiting the opposite face.

**Hint:** Recall the formula for electric flux: Φ = E * A * cos(θ).

### Step 4: Applying Gauss's Law
According to Gauss's Law, the net electric flux through a closed surface is proportional to the charge enclosed within that surface. If the net flux through the cube is zero, it implies that the net charge enclosed within the cube is also zero.

**Hint:** Gauss's Law states that the net flux (Φ) through a closed surface is related to the enclosed charge (Q) by the equation: Φ = Q/ε₀, where ε₀ is the permittivity of free space.

### Step 5: Conclusion
Since the electric flux through the imaginary cube in a uniform electric field is zero (flux in equals flux out), we conclude that the net charge within the cube is indeed zero.

**Final Answer:** The statement is **True**.