The correct option for the question regarding the definition and calculation of electric flux through a surface in a uniform electric field is: **D. Electric flux is calculated as the product of the electric field strength, the surface area, and the cosine of the angle θ.** ### Detailed Explanation **1. Understanding Electric Flux:** Electric flux (Φ_E) is a measure of the quantity of electric field lines passing through a given surface. It is a crucial concept in electromagnetism and is defined mathematically as: \[ \Phi_E = \int \vec{E} \cdot d\vec{A} \] Where: - \(\Phi_E\) is the electric flux, - \(\vec{E}\) is the electric field vector, - \(d\vec{A}\) is the differential area vector (which has a magnitude equal to the area and points normal to the surface). **2. Simplifying the Calculation:** For a uniform electric field, the electric field strength (E) is constant across the surface. If we consider a flat surface with area (A) and the angle (θ) between the electric field lines and the normal to the surface, we can simplify the integral. The dot product \(\vec{E} \cdot d\vec{A}\) can be expressed as: \[ \vec{E} \cdot d\vec{A} = E \cdot A \cdot \cos(\theta) \] Thus, the total electric flux through the surface becomes: \[ \Phi_E = E \cdot A \cdot \cos(\theta) \] This formula shows that the electric flux depends on the strength of the electric field, the area of the surface, and the cosine of the angle between the electric field and the normal to the surface. **3. Why Option D is Correct:** Option D correctly states that electric flux is calculated as the product of the electric field strength, the surface area, and the cosine of the angle θ. This aligns perfectly with the derived formula for electric flux in a uniform electric field. ### Analysis of Other Options **Option A: [blank]** - Since this option is blank, it cannot be evaluated. **Option B: Electric flux is independent of the angle and is given by the product of the electric field strength and the surface area.** - This option is incorrect because it ignores the angle θ. The angle is crucial in determining how much of the electric field actually passes through the surface. If the angle is 90 degrees, for example, the flux would be zero because the electric field lines are parallel to the surface and do not penetrate it. Therefore, electric flux is not independent of the angle. **Option C: [blank]** - Since this option is also blank, it cannot be evaluated. ### Common Pitfalls - **Ignoring the Angle:** A common mistake is to assume that the electric flux is simply the product of the electric field strength and the area without considering the angle. Always remember to include the cosine of the angle. - **Confusing Area Vector Direction:** The area vector \(d\vec{A}\) must be directed outward from the surface. If you mistakenly point it in the opposite direction, the sign of the flux will be incorrect. - **Non-Uniform Fields:** The formula derived is specifically for uniform electric fields. In cases of non-uniform fields, the calculation of electric flux would require integration over the surface. ### Revision Summary - Electric flux (Φ_E) measures the number of electric field lines passing through a surface. - The formula for electric flux in a uniform electric field is \(\Phi_E = E \cdot A \cdot \cos(\theta)\). - The angle θ is crucial; it affects how much of the electric field contributes to the flux. - Always ensure the area vector is correctly oriented when calculating electric flux.