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.
Consider a plane surface of area 50 mm2 in a uniform electric field of magnitude 25 N/C. The angle between the electric field and the normal to the surface is φ. Determine the values of angle φ for which the electric flux magnitude through the surface is i) maximum or ii) minimum.
A planar square surface with an area of 0.300 m2 is immersed in a uniform electric field of magnitude 20 N/C. The normal to the square surface forms an angle of φ = 45° with the electric field. i) Calculate the electric flux (ΦE) through the surface. ii) Why is the electric flux independent of the geometrical shape of the 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.
Visualize a cuboid with a side length of s, symmetrically positioned around a long line of charge. This line of charge has a linear charge density denoted by Q/L, as illustrated in the subsequent diagram. (i) Formulate an equation for the electric flux that traverses the upper surface of the cuboid, which is parallel to the xy-plane. This equation should be expressed in terms of Q/L and the dimensions of the cuboid. (ii) Subsequently, calculate the total flux passing through the cuboid. Bear in mind that the electric field penetrating the surface is not constant; it varies in both direction and intensity, depending on its relative position to the line of charge.