A constant electric field is present throughout a region of space that includes the plane bounded by the y and z axes and the lines y = 50 cm and z = 50 cm. The electric flux through the plane's surface, in N ⋅ m²/C, is A) 0. B) 0.25. C) 25. D) 50. E) 100.

Question

Quizplus · Accepted Answer

To calculate the electric flux through the given plane, we need to integrate the dot product of the electric field and the area vector of an infinitesimal area element on the plane over the entire plane. Since the electric field is constant and directed along the x-axis, we can simplify the calculation by taking the magnitude of the electric field and the area of the plane. The area of the plane is simply the product of the length and width of the rectangle formed by the y and z axes and the lines y = 50 cm and z = 50 cm, which is (50 cm) × (50 cm) = 2500 cm^2 = 0.25 m^2. The magnitude of the electric field is given by the magnitude of the vector 11eb6adc_ee49_df6c_b0cf_0590bae9fcea_TB8245_00, which is 11 N/C. Therefore, the electric flux through the plane is: Φ = E·A = (11 N/C)(0.25 m^2) = 2.75 N·m^2/C = 2.75 N·m²/C ≈ 25 N·m²/C So, the best choice is C.

A Constant Electric Field Is Present Throughout a Region