Consider a thin nonconducting ring of radius R, as shown below, which has a charge Q uniformly spread out on it. (a) In the DEVELOP step, derive an expression for the electric force on a point charge q placed at a point P, which is located on the axis of the ring a distance x from the center. (b) Then, let x=R= 6.0 cm and Q = q = + 6.0 μC, and in the EVALUATE step, calculate the magnitude (in N) and describe the direction of the electric force on the charge at point P. boit فلد R P

Consider a point charge q =+22e is located at the origin. Calculate the magnitude and direction of the electric field at the field point with coordinates (–0.345, –0.500) nm. Please include a conclusion for the problem.

The figure shows two concentric rings, of radii R and R' = 4.23R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.25R from the center of the rings. The smaller ring has uniformly distributed charge Q = 6.82 × 10-6 C. What is the uniformly distributed charge on the larger ring if the net electric field at P is zero?

point charge of 40 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 5 cm) which has a net charge of -70 nC. Determine the resulting charge density on the outer surface of the conducting sphere.

A solid insulating sphere of radius R =5.00 cm has a non-uniform charge density p = Por2, where r is measured from the center of the sphere and po is constant. Concentric with this sphere is a conducting spherical shell with inner radius a = 7.00 cm and outer radius b = 9.00 cm, having a net charge q = -1.00 µC. a) Find the value for the constant po (including units), given that the total charge on the insulating sphere is Q = 4.00 nC. Be sure to first derive expression in symbolic form in terms of Q, R. Box both the symbolic expression and the final answer. b) Derive an expression for electric field forr b. Box it. e) Draw an E vs. r graph and show the values for E at distances R, a, b.

(a) Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Suggestion: Use the following expression and treat the cylinder as a collection of ring charges. (Use any variable or symbol stated above along with the following as necessary: ke.) E = кех (x² + a²j3/20 E = R (b) Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the following expression to find the field it creates at the same point. (Use any variable or symbol stated above along with the following as necessary: k.) X 2xk, 0 (1 - (2²+42²271/72) 2лk d

Given that D = 10 x 3 3 a x(μC/m2), determine the total charge (in microcoulombs) enclosed in a cube of 2 m on an edge, centered at the origin and with edges parallel to the axes.

In free space, a linear charge density > is on the z axis. Get the electric force over a unit charge "q" located at P (1, 2, 3) m if the linear charge density is in -4 m < z < 4m = 2μC m Give the answer in unit vectors terms.

In Figure (a) below, a particle of charge +Q produces an electric field of magnitude Epart at point P, at distance R from the particle. In Figure (b), that same amount of charge is spread uniformly along a circular arc that has radius R and subtends an angle 8. The charge on the arc produces an electric field of magnitude Earc at its center of curvature P. For what value of 0 (in º) does Earc = 0.75Epart? (Hint: You will probably resort to a graphical solution.) +Q |▬▬▬R—-|| Number i P (a) AR +Q}/0/2/ (b) Units ° (degree:

In Figure (a) below, a particle of charge +Q produces an electric field of magnitude Epart at point P, at distance R from the particle. In Figure (b), that same amount of charge is spread uniformly along a circular arc that has radius R and subtends an angle 8. The charge on the arc produces an electric field of magnitude Earc at its center of curvature P. For what value of 0 (inº) does Earc = 0.75Epart? (Hint: You will probably resort to a graphical solution.) +Q ||▬▬R—-| Number i P (a) ! +Q{{0/2 VR 8/24 (b) Units O (degree