A cylindrical surface shown in the figure below is defined by its radius R=8.1 cm and length h=67 cm. The positive direction of the normal to this surface is chosen as outward. As also shown in the figure, this surface is situated in the region of the uniform electric field of magnitude E=3.1 kN/C. E Αν B h (a) (b) E 00 (a) Find the flux (including its algebraic sign) of this electric field through the "left half" of the cylindrical surface defined by a cut-off through the shown points A, B, C, D in configuration (a), where the cylindrical axis is oriented vertically: Φ= ☐ N-m2/C. (b) Find now the flux of this field through the same half of the cylindrical surface in configuration (b), where the cylindrical axis is tilted "towards" the electric field direction by angle 0=30° from the vertical: Ф= N⚫m2/C.

dx P. ++ + + + + + dq L Evaluate an expression for the electric field at point P of a uniformly charged rod with linear charge density, 2 [C/m2], as shown above. Hint: The integral will be of the form: E (P) = [ k dq , where dq = 1 dx x2 1

could you solve (d) only please?

Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as shown in the figure below. Calculate the electric flux through the closed surface. y E L L We need to solve for the electric flux through each face of the cube and take the sum to calculate the net electric flux: Фnet Ф1 + Ф, +Ф; + Ф. ху + 0xz+@yz The flux through surface 1 is: 01=0. The flux through surface 2 is: 02= The flux through surface 3 is: 03 = The flux through the surface on the xy plane is: Oxy = The flux through the surface on the xz plane is: Oxz= The flux through the surface on the yz plane is: O yz Taking the algebraic sum, the net electric flux through the cube is: Onet = 1111

A total charge 7.1 ✕ 10−6 C is distributed uniformly throughout a cubical volume whose edges are 8.0 cm long. What is the electric flux (in N · m2/C) through a spherical surface of radius 4.0 cm that is also concentric with the charge distribution?

Consider a closed triangular box resting within a horizontal electric field of magnitude E = 8.26 104 N/C as shown in the figure below. (a) Calculate the electric flux through the vertical rectangular surface of the box.