A point charge is placed at each corner of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are neg- ative, as shown in Fig. E21.30. What is the direction of the net electric field at the center of the square due to the four charges, and what is its mag- 21.30 .. Figure E21.30O +q +q a a nitude in terms of q and a? 21 31 Two point charges are sena
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- A charge q1=+2q is at the origin, and a charge q2=−q is on the x-axis at x=a, where a>0. Find the expression Ex<0 for the total electric field on the x-axis in the region x<0. Use k to represent Coulomb's constant. Find the expression E0<x<a for the total electric field on the x-axis in the region 0<?<?. Find the expression Ea<x for the total electric field on the x-axis in the region ?<?. Determine all the points x on the x-axis where the electric field is zero. If there is more than one point, enter them as a comma‑separated list.A +7 nC charge is located 3.2 meters to the right of a +6 nC charge. Determine the magnitude of the electric field at the midpoint of the two charges. Express your answer as a positive number in N/C.17.6. A charged cork ball of mass 1.10 g is suspended on a light string in the presence of a uniform electric field as shown in the figure below. When E = (2.80 î + 5.20 ĵ) ✕ 105 N/C, the ball is in equilibrium at θ = 37.0°. (a) Find the charge on the ball. C(b) Find the tension in the string. N
- 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 in Figure E23.1. 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.…Could you solve the question in the picture below?Three equal positive charges are at the corners of an equilateral triangle of side a as in Figure P15.34. Assume the three charges together create an electric field. (a) Sketch the electric field lines in the plane of the charges. (b) Find the location of one point (other than) where the electric field is zero. What are (c) the magnitude and (d) the direction of the electric field at p due to the two charges at the base?
- Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium, they are a distance d apart (Fig. P22.44). (a) Determine the charge q on each bead. (b) Determine the charge required for d to become equal to 2RThree equal positive charges are at the corners of an equilateral triangle of side a as in Figure P15.38. Assume the three charges together create an electric field. (a) Sketch the electric field lines in the plane of the charges. (b) Find the location of one point (other than ∞) where the electric field is zero. What are (c) the magnitude and (d) the direction of the electric field at P due to the two charges at the base?A conducting sphere is placed within a conducting spherical shell. The conductors are in electrostatic equilibrium. The inner sphere has a radius of 1.50 cm, the inner radius of the spherical shell is 2.25 cm, and the outer radius of the shell is 2.75 cm. The inner sphere has a charge of 228 nC and the spherical shell has zero net charge. What is the electric field at a point 3.80 cm from the center? Enter a positive answer if the electric field is directed away from the center and a negative answer if the electric field is directed toward the center.
- Review Conceptual Example 11 before attempting to work this problem. Four charges with equal magnitudes of 9.24 x 10-12 Care placed at the corners of a rectangle. The lengths of the sides of the rectangles are 3.23 cm and 6.21 cm. Find the magnitude of the electric field at the center of the rectangle in Figures a and b. (a) Number (b) Number i i 2, E13 E24 E24 44 3 +9 +9 +9 4 +4 Units Units (b) +9Review Conceptual Example 11 before attempting to work this problem. Four charges with equal magnitudes of 9.88 × 10-¹2 Care placed at the corners of a rectangle. The lengths of the sides of the rectangles are 3.20 cm and 4.56 cm. Find the magnitude of the electric field at the center of the rectangle in Figures a and b. (a) Number i (b) Number i +9 +9 1 (a) Units Units 2, E24 3 +9 E13 E C (b) E24 +qA thin disk with a circular hole at its center, called an annulus, has inner radius R₁ and outer radius R₂ (Fig. P21.87). The disk has a uniform positive surface charge density o on its surface. (a) Determine the total electric charge on the annulus. (b) The annulus lies in the yz-plane, with its center at the origin. For an arbitrary point on the x-axis (the axis of the annulus), find the magnitude and direction of the electric field E. Figure P21.87 IR₁ X Consider points both above and below the annulus. (c) Show that at points on the x-axis that are sufficiently close to the origin, the magnitude of the electric field is approximately proportional to the distance between the center of the annulus and the point. How close is "sufficiently close"? (d) A point particle with mass m and negative charge -q is free to move along the x-axis (but cannot move off the axis). The particle is originally placed at rest at x = 0.01 R₂ and released. Find the frequency of oscillation of the…