The magnitude of the net electric field at a distance x from the center and on the axis of a uniformly charged ring of radius r and total charge q is given by  Enet =  kqx (x2 + r2)3/2.  Consider two identical rings of radius 12.0 cm each, located as shown in the diagram below. The charge per unit length on each ring is +3.90 nC/cm and  d = 26.0 cm.  What is the magnitude of the net electric field at the center of ring B?

The figure is a section of a conducting rod of radius R₁ = 1.50 mm and length L = 12.10 m inside a thin-walled coaxial conducting cylindrical shell of radius R₂ = 11.8R₁ and the (same) length L. The net charge on the rod is Q₁ = +3.62 × 10-12 C; that on the shell is Q2 = -2.0501. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.13R₂? What are (c) E and (d) the direction at r = 5.12R₁? What is the charge on the (e) interior and (f) exterior surface of the shell? R₂ R₁

2 narrow, flat metal plates are positioned vertically, 20.00 cm. The first plate has a positive charge with charge density σ=+630.0 mC/m2 and a second plate has an equal but opposite negative charge with charge density σ=-6300.0 mC/m2 . There are also two narrow, flat metal plates positioned horizontally, 30.00 cm apart, with the top plate given a negative charge, and the bottom plate given an equal but opposite positive charge, such that the electric potential of the bottom plate is 5.00 V higher than the top plate. A small sphere with a mass of m =64.35 g, and a charge of q =22.00 mC is attached to a narrow, stiff, massless, insulating rod with a length of L= 8.00 cm, which is pivoted at point O, which is 2.000 cm from the second plate. The sphere/rod unit is angled at 5 degrees with horizontal and released from rest. Will the sphere/rod ever hit an angle of 0 degrees with the horizontal? If so, how long will it take to reach that point?

Consider the symmetrically arranged charges in the figure, in which qa 9b = -2.45 µC and q. = qd = +2.45 µC. Determine the direction of the electric field at the location of charge q. O right up and left down and left up and right dn down left down and right Calculate the magnitude of the electric field E at the location of q given that the square is 6.35 cm on a side.

There are two concentric cylinders with R1= 0.0056 m and R2= 8R1 with a length of 6.1m. The internal cylinder charge is q=2.7nC and uniformly distributed, the external one is -3q also uniformly distributed. How much is the electric field at r= 4.4R1. Express your answer in N/A to three significant figures.

The figure below shows a small, charged bead, with a charge of q = +42.0 nC, that moves a distance of d = 0.189 m from point A to point B in the presence of a uniform electric field  E  of magnitude 270 N/C, pointing right. A positive point charge q is initially at point A, then moves a distance d to the right to point B. Electric field vector E points to the right. (a) What is the magnitude (in N) and direction of the electric force on the bead? magnitude Ndirection     (b) What is the work (in J) done on the bead by the electric force as it moves from A to B?  J (c) What is the change of the electric potential energy (in J) as the bead moves from A to B? (The system consists of the bead and all its surroundings.) PEB − PEA =  J (d) What is the potential difference (in V) between A and B? VB − VA =  V