The figure below shows two concentric rings, of radii R and R' = 3R, that lie on the same plane. Point P lies on the central r-axis, at distance D = 2R from the center of the rings. The smaller ring has uniformly distributed charge +Q. In terms of +Q, what is the uniformly distributed charge on the larger ring if the net electric field at P is zero? (modified from Halliday et al., 2015, Chapter 22, Problem 30). y P R' D
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- In the figure a small, nonconducting ball of mass m = 0.99 mg and charge q = 2.1 × 10*8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle 0 = 37° with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surfaçe charge density o of the sheet. m, 4 i Units NumberThe electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below. E = 2zk, o 1- (2 + R?)1/2 Show that the electric field at distances x that are large compared with R approaches that of a particle with charge O = aTR2. Suggestion: First show that x/(x2 + R2)1/2 = (1+ R2/x2)-1/2, and use the binomial expansion (1 + 8)" 1 + nổ when 8 « 1. (Do this on paper, Your instructor may ask you to turn in this work.) Filters Add a caption...An infinite sheet lie on the xz plane and z axis points outward from the page (not shown). A solid non-conducting sphere of radius R is placed at h+r distance away from the infinite sheet. Use the following values of these quantities charge density of sphere ρ=44pC/m^3, the charge density of the infinite sheet σ=−20pC/m^2, the radius of the solid sphere R=4.0m, the radius of the Gaussian sphere r=8.0m value of h=2.0m. (here 1pC means pico coulomb charge that is, 10^−12C.) Step 1 Consider the infinite sheet only for this step a) Find the magnitude of the electric field at points P1 and P2 due to infinite sheet only. (Note: the magnitude of a vector is a positive quantity.) b) Find the net flux through the Gaussian sphere of radius r due to infinite sheet only. Step 2 Consider the solid non-conducting sphere only for this step c) Find the net flux through the Gaussian sphere of radius r due to the solid sphere only.
- Consider a thin plastic rod bent into an arc of radius R and angle a. The rod carries a uniformly distributed negative charge -Q. (Note: the diagram may have the incorrect sign.) y α R -Q X What is the x component of the electric field at the origin? (Enter your responses in terms of the symbolic quantities mentioned in the problem. To make things easier, just write the letter "a" for the angle a, and use the Coulomb constant k rather than the unwieldy 1/4no.) Ex = k*Q*sin(a)/(a*R^2) Computer's answer now shown above. Tries 0/6 What is the y component of the electric field at the origin? Ey = k*Q*(1-cos(a))/(a*R^2) Computer's answer now shown above. Tries 0/6 Follow the steps outlined in class and in the textbook: 1. Use a diagram to explain how you'll cut up the charge distribution, and draw the AE contributed by a representative piece of charge at a given location. 2. Express algebraically the contribution each piece makes to each vector component of the electric field. Indicate…A plastic rod with linear charge density λ is bent into the quarter circle shown in (Figure 1). We want to find the electric field at the origin. Express your answer in terms of the variables R, λ, unit vectors i^, j^, constant π, and permittivity constant ϵ0.Needs Complete typed solution with 100 % accuracy.
- Assume a uniformly charged ring of radius R and charge Q produces an electric field E ringat a point P on its axis, at distance x away from the center of the ring as in Figure a. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius as in Figure b. How does the field E disk produced by the disk at P compare with the field produced by the ring at the same point?Assume you have a line of positive charge with a linear charge density of 10.0 µC/m. Assume that this line of charge is infinitely long and lies on the z-axis (which is perpendicular to both the x- and y-axes). a) Find the strength and direction of the electric field associated with this line of charge at (0.5 m, 0 m, 0 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z b) Find the strength and direction of the electric field associated with this line of charge at (0 m, 0.5 m, 5 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z c) Find the strength and direction of the electric field associated with this line of charge at (2.0 m, 0 m, Om) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+zla Given A = 17 [80°] and B = 13 [159°], the cross product B x A is Round your answer to the nearest tenth and make sure to include the sign if your answer is in the negative z-direction. Your Answer: Answer b Several point charges are located within a closed Gaussian surface, S, and several point charges are located just outside of the Gaussian surface. The magnitude of each charge is equal q and the number of positive and negatives charges in each of the respective regions are shown below. What is the electric flux, E = f. Ē · dã, given by Gauss' law through the closed surface S? Not uniform along S as the charge is not uniform A line of charge with linear charge density i = 29 nC/m is enclosed in a Gaussian cylinder with height h = 18.2 mm and radius r = 4.3 mm as shown below. What is the magnitude of the total electric flux passing through the cylinder in Nm2/C? Round your answer to the nearest whole number. Your Answer:
- You are working at a technology company. You have been given a task of designing a very small device that will act as an oscillator to control an optical system. The device is constructed as follows. A particle of mass m and charge -g is placed at the center of a uniformly charged ring, where the ring has a total positive charge Q as shown in the figure below. The particle, confined to move along the x-axis, is moved by an external uniform electric field a small distance x along the axis (where x « a), where it remains in equilibrium. The external field is then turned off and the particle oscillates along the x-axis on either side of the center of the ring. Your supervisor observes your prototype and decides that the oscillation frequency of the charge needs to be increased by a factor of 8. (a) Which parameter-m, q, Q, or a-can be changed by the smallest percentage to achieve the desired frequency? m a (b) Determine the percentage change. (Enter the magnitude.) %A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r < a. (b) From this value, find the magnitude of the electric field for r < a. (c) What charge is contained within a sphere of radius r when a < r < b? (d) From this value, find the magnitude of the electric field for r when a < r < b. (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r ? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these…A small plastic ball of mass m = 1.50 g is suspended by a string of length L = 17.0 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a ? = 17.0° angle with the vertical as indicated, what is the net charge on the ball? A ball of mass m is attached to a string of length L and suspended from the ceiling. The string makes an acute angle ? with the normal line from the ceiling, such that the string and ball are displaced to the right of the normal line. To the right of the string and ball, five parallel, evenly-spaced, identical arrows point to the right. The arrows are vertically stacked and labeled with E = 1.00 ✕ 103 N/C. To the left of the string and ball, x y-coordinate axes demonstrate that the +x-axis points to the right and the +y-axis points up.