Problem 1
A flat sheet of paper of area 0.250 m\(^2\) is oriented so that the normal to the sheet is at an angle of 60\(^\circ\) to a uniform electric field of magnitude 14 N/C. (a) Find the magnitude of the electric flux through the sheet. (b) Does the answer to part (a) depend on the shape of the sheet? Why or why not? (c) For what angle \(\phi\) between the normal to the sheet and the electric field is the magnitude of the flux through the sheet (i) largest and (ii) smallest? Explain your answers.
Problem 2
A flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. The sheet is immersed in a uniform electric field of magnitude 90.0 N/C that is directed at 20\(^\circ\) from the plane of the sheet (\(\textbf{Fig. E22.2}\)). Find the magnitude of the electric flux through the sheet.
Problem 3
You measure an electric field of 1.25 \(\times\) 10\(^6\) N/C at a distance of 0.150 m from a point charge. There is no other source of electric field in the region other than this point charge. (a) What is the electric flux through the surface of a sphere that has this charge at its center and that has radius 0.150 m? (b) What is the magnitude of this charge?
Problem 4
It was shown in Example 21.10 (Section 21.5) that the electric field due to an infinite line of charge is perpendicular to the line and has magnitude \(E = \lambda/2\pi\varepsilon_0r\). Consider an imaginary cylinder with radius \(r =\) 0.250 m and length \(l =\) 0.400 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is \(\lambda =\) 3.00 \(\mu\)C/m. (a) What is the electric flux through the cylinder due to this infinite line of charge? (b) What is the flux through the cylinder if its radius is increased to \(r =\) 0.500 m? (c) What is the flux through the cylinder if its length is increased to \(l =\) 0.800 m?
Problem 9
A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of -49.0 \(\mu\)C. Find the electric field (a) just inside the paint layer; (b) just outside the paint layer; (c) 5.00 cm outside the surface of the paint layer.
Problem 10
A point charge \(q_1 =\) 4.00 nC is located on the \(x\)-axis at \(x =\) 2.00 m, and a second point charge \(q_2 = -\)6.00 nC is on the \(y\)-axis at \(y =\) 1.00 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius (a) 0.500 m, (b) 1.50 m, (c) 2.50 m?
Problem 11
A 6.20-\(\mu\)C point charge is at the center of a cube with sides of length 0.500 m. (a) What is the electric flux through one of the six faces of the cube? (b) How would your answer to part (a) change if the sides were 0.250 m long? Explain.
Problem 12
The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4 \(\times\) 10\(^{-15}\) m. (a) What is the electric field this nucleus produces just outside its surface? (b) What magnitude of electric field does it produce at the distance of the electrons, which is about 1.0 \(\times\) 10\(^{-10}\) m? (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?
Problem 13
Two very long uniform lines of charge are parallel and are separated by 0.300 m. Each line of charge has charge per unit length +5.20 \(\mu\)C/m. What magnitude of force does one line of charge exert on a 0.0500-m section of the other line of charge?
Problem 14
A solid metal sphere with radius 0.450 m carries a net charge of 0.250 nC. Find the magnitude of the electric field (a) at a point 0.100 m outside the surface of the sphere and (b) at a point inside the sphere, 0.100 m below the surface.
