Exam Question:

A rectangular wire loop with sides of lengths 10 cm and 5 cm is placed in a uniform electric field E = 500 N/C directed downward. The loop is parallel to the electric field lines and lies in the xy-plane such that the longer side of the loop is aligned along the x-axis. Calculate the electric flux passing through the loop.

Answer:

The electric flux passing through the loop is given by the formula:

Φ = EA cosθ

where Φ is the electric flux, E is the electric field strength, A is the area, and θ is the angle between the electric field and the normal to the surface.

In this case, the electric field is directed downward, and the loop lies parallel to the electric field lines. Therefore, the angle between the electric field and the normal to the surface is 0 degrees (cos 0 = 1).

The area of the loop is given by the product of its sides:

A = length × width

A = 10 cm × 5 cm = 50 cm²

To convert the area to square meters, we divide by 10,000:

A = 50 cm² ÷ 10,000 = 0.005 m²

Now, we can calculate the electric flux:

Φ = EA cosθ

Φ = (500 N/C) × (0.005 m²) × cos 0°

Φ = 2.5 Nm²/C

Therefore, the electric flux passing through the loop is 2.5 Nm²/C.

Note: It is important to use the correct units for all quantities and to ensure that the length and width are expressed in the same unit before calculating the area.