Problem 15
How many excess electrons must be added to an isolated spherical conductor 26.0 cm in diameter to produce an electric field of magnitude 1150 N/C just outside the surface?
Problem 17
A very long uniform line of charge has charge per unit length 4.80 \(\mu\)C/m and lies along the \(x\)-axis. A second long uniform line of charge has charge per unit length -2.40 \(\mu\)C/m and is parallel to the x-axis at \(y =\) 0.400 m. What is the net electric field (magnitude and direction) at the following points on the \(y\)-axis: (a) \(y =\) 0.200 m and (b) \(y =\) 0.600 m?
Problem 18
The electric field 0.400 m from a very long uniform line of charge is 840 N/C. How much charge is contained in a 2.00-cm section of the line?
Problem 19
A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37 \(\times\) 10\(^{-6}\) C/m\(^2\). A charge of -0.500 \(\mu\)C is now introduced at the center of the cavity inside the sphere. (a) What is the new charge density on the outside of the sphere? (b) Calculate the strength of the electric field just outside the sphere. (c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?
Problem 20
(a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere? (b) At a distance of 0.200 cm from the axis of a very long charged conducting cylinder with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the axis of the cylinder? (c) At a distance of 0.200 cm from a large uniform sheet of charge, the electric field is 480 N/C. What is the electric field 1.20 cm from the sheet?
Problem 21
The electric field at a distance of 0.145 m from the surface of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it? (b) Calculate the electric field inside the sphere at a distance of 0.200 m from the center.
Problem 22
A point charge of -3.00 \(\mu\)C is located in the center of a spherical cavity of radius 6.50 cm that, in turn, is at the center of an insulating charged solid sphere. The charge density in the solid is \(\rho =\) 7.35 \(\times\) 10\(^{-4}\) C/m\(^3\). Calculate the electric field inside the solid at a distance of 9.50 cm from the center of the cavity.
Problem 23
An electron is released from rest at a distance of 0.300 m from a large insulating sheet of charge that has uniform surface charge density +2.90 \(\times\) 10\(^{-12}\) C/m2. (a) How much work is done on the electron by the electric field of the sheet as the electron moves from its initial position to a point 0.050 m from the sheet? (b) What is the speed of the electron when it is 0.050 m from the sheet?
Problem 24
Charge \(Q\) is distributed uniformly throughout the volume of an insulating sphere of radius \(R =\) 4.00 cm. At a distance of \(r =\) 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude \(E =\) 940 N/C. What are (a) the volume charge density for the sphere and (b) the electric field at a distance of 2.00 cm from the sphere's center?
Problem 26
A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area \(\sigma =\) 5.00 \(\times\) 10\(^{-6}\) C/m\(^2\). (a) A small sphere of mass \(m =\) 8.00 \(\times\) 10\(^{-6}\) kg and charge \(q\) is placed 3.00 cm above the sheet of charge and then released from rest. (a) If the sphere is to remain motionless when it is released, what must be the value of \(q\)? (b) What is \(q\) if the sphere is released 1.50 cm above the sheet?
