Chapter 22. The Electric Field II: Continuous Charge Distributions Calculating E From Coulomb's Law 1. A uniform line charge that has a linear charge density equal to 3.5 nC/m is on the x axis between x = 0 and x = 5.0 m. (a) What is its total charge? Ans: 17.5nC 2. A charge of 2.75 C is uniformly distributed on a ring of radius 8.5 cm. Find the electric field strength on the axis at distances of (a) 1.2 cm, (b) 3.6 cm, and (c) 4.0 m from the center of the ring. Ans: (a) 4.7x105N/C (b) 1.1x10N/C (c) 1.5x103N/C Gauss's law and it's Applications 3. Find the value of the electric field at a distance r= 10 cm from the center of a non conducting sphere of radius R= 1 cm which has an extra positive charge equal to 7 C uniformly distributed within the volume of the sphere. Ans: E = 6.3 10 N/C 4. Find the flux through a spherical Gaussian surface of radius a = 1 m surrounding a charge of 8.85 pc. Ans: flux = 1Nm/C 5. A cylindrical metal can has a height of 27cm and a radius of 11 cm. The electric field is directed outward along the entire surface of the can (including the top and bottom), with a uniform magnitude of 4x10N/ C. How much charge does the can contain? 6. A 6nC point charge is located at the center of a cube of side length 2m. What is the electric flux through each of the faces of the cube? 7. A spherical ball of plasma has a radius of 0.5m. The electric field on the surface of the ball is measured to be 8.9x10N/C and points radially inward toward the center. What is the average volume charge density of the plasma? Ans: 4.72 10-7C/m 8. A 4cm-square sits in a uniform electric field of 5N/C, Find the electric flux through the square. Ans = 18 10-3 Nm/C 9. A thundercloud produces a vertical electric field of magnitude 28 kN C at ground level. You hold a 22cm x 28cm sheet of paper horizontally below the cloud. (a) What is the electric flux through the sheet? (b) What would the flux be if you tilt the sheet of paper by 30 degree (c) What would the flux be if you hold the sheet of paper vertically? (a) = 1.72 10 Nm/C (b) = 1.49 Nm/C (c) zero Electric charge and field at conductor surface -Worksheet 10. An uncharged penny is in an external electric field of magnitude 1.6 kN/C directed perpendicular to its faces. (a) Find the charge density on each face of the penny, assuming the faces are planes. (b) If the radius of the penny is 1 cm, find the total charge on one face. Ans: (a) = 2.832 10-8 c/m (b) = 8.893 1012 C 11. An uncharged metal slab has square faces with 12-cm sides. It is placed in an external electric field that is perpendicular to its faces. The total charge induced on one of the faces is 1.2 nC. What is the magnitude of the electric field? Ans: E = 9416.2 N/C 12. A charge of 6 DC is placed uniformly on a square sheet of nonconducting material of side 20 cm (a) What is the surface charge density o? Ans: = 1.5 10-7C/m