Electric Flux Practice Problems
A curved lens is placed in a uniform electric field, E. The radius of the flat circular area on the left of the lens is R. The optical lens axis is parallel to the field's direction as shown in the image. Find out the electric flux through the curved surface.
Given a cuboid-shaped room with uniform electric fields across all faces, a negatively charged object is placed at the center of the room as shown. The back face of the room has a missing electric field vector. Determine the direction of the missing vector, i.e., inward or outward, and calculate the minimum strength needed to maintain uniformity inside the room.
Consider a sphere of radius R centered on a long thin wire with linear charge density λ. The flux through a small area on the sphere is not simply EA because the electric field varies in both magnitude and direction in this scenario. But you can compute the flux by performing the flux integral. Consider a small area dA on the sphere's surface. Define dA as a small patch with area dθdφR² (in spherical coordinates), with the vector pointing radially outward. One such patch is located at position θ (the angle from the z-axis). Use the known electric field of a wire to calculate the electric flux dΦ through this small area.
