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- A very large disk lies horizontally and has surface charge density = 2.3 nC/m2. An electron is released at the surface. (It begins from rest and moves vertically upward.) Ignoring gravity, find the speed of the electron when it is 1.0 mm above the disk.A very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?A potassium chloride molecule (KCl) has a dipole moment of 8.9 1030 Cm. Assume the KCl molecule is in a uniform electric field of 325 N/C. What is the change in the systems potential energy when the molecule rotates a. from = 170 to 180, b. from = 90 to 100, and c. from = 10 to 0?
- Figure P24.17 shows a dipole. If the positive particle has a charge of 35.7 mC and the particles are 2.56 mm apart, what is the electric field at point A located 2.00 mm above the dipoles midpoint?Review. Two insulating spheres have radii r1 and r2, masses m1 and m2, and uniformly distributed charges q1 and q2. They are released from rest when their centers are separated by a distance d. (a) How fast is each moving when they collide? (b) What If? If the spheres were conductors, would their speeds be greater or less than those calculated in part (a)? Explain.An electron is in a uniform upward-pointing electric field. a. If the electron experiences a downward acceleration of 9.81 m/s2, what is the magnitude of the electric field? (Ignore gravity.) b. What is the gravitational force on this electron? Is it okay to ignore gravity? Explain.
- A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with axes that coincide. The wire has charge per unit length = 20, and the hollow cylinder has net charge per unit length = 30. Use Gausss law to answer these questions: What are the charges per unit length on a. the inner surface and b. the outer surface of the hollow cylinder? c. What is the electric field a radial distance d from the axis of the coaxial cable?Given the two charged particles shown in Figure P24.11, find the electric field at the origin.Often we have distributions of charge for which integrating to find the electric field may not be possible in practice. In such cases, we may be able to get a good approximate solution by dividing the distribution into small but finite particles and taking the vector sum of the contributions of each. To see how this might work, consider a very thin rod of length L = 16 cm with uniform linear charge density = 50.0 nC/m. Estimate the magnitude of the electric field at a point P a distance d = 8.0 cm from the end of the rod by dividing it into n segments of equal length as illustrated in Figure P24.21 for n = 4. Treat each segment as a particle whose distance from point P is measured from its center. Find estimates of EP for n = 1, 2, 4, and 8 segments. FIGURE P24.21
- A When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Lets see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2 carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance above the midpoint of the rod using each of two methods: a. modeling the rod with just two particles and b. using the exact expression E=kQy12+y2 c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression. FIGURE P24.77 Problems 77 and 78.A charged rod is curved so that it is part of a circle of radius R (Fig. P24.32). The excess positive charge Q is uniformly distributed on the rod. Find an expression for the electric field at point A in the plane of the curved rod in terms of the parameters given in the figure.Figure P24.16 shows three charged particles arranged in the xy plane at the coordinates shown, with qA = qB = 3.30 nC and qC = 4.70 nC. What is the electric field due to these particles at the origin? FIGURE P24.16