An average human weighs about 700 N. Part A If two such generic humans each carried 2.0 coulomb of excess charge, one positive and one negative, how far apart would they have to be for the electric attraction between them to equal their 700 N weight? Express your answer using two significant figures. r = km
Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -2.00 nC and is at x = 3.50 cm. Charge q1 is at x = 1.00 cm. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Vector addition of electric forces on a line. Part A What is q1 (magnitude and sign) if the net force on q3 is zero? Express your answer in nanocoulombs. Q1 = nC
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 negative, as shown in the following figure. (Figure 1) Figure 1 of 1 Part A What is the direction of the net electric field at the center of the square? rightward direction upward direction leftward direction downward direction Part B What is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a? Express your answer in terms of the variables q, a, and appropriate constants. E=
The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. Part A What charge would a human with a mass of 58.0 kg have to acquire to overcome his or her weight by the force exerted by the earth’s electric field? AΣφ Q = C Part B What would be the magnitude of the repulsive force between two people each with the charge calculated in part A and separated by a distance of 180 m? √ AΣφ F = N
An electron is projected with an initial speed v0 = 1.70 × 10^6 m/s into the uniform field between the parallel plates in ( Figure 1). Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Electron in a uniform field. Figure 1 of 1 Part A If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. Express your answer in newtons per coulomb. Part B Suppose that in the figure the electron is replaced by a proton with the same initial speed v0. Would the proton hit one of the plates? yes no Part C If the proton would not hit one of the plates, what would be the magnitude of its vertical displacement as it exits the region between the plates? Express your answer in meters. Part D What would be the direction of proton’s displacement? displacement is upward displacement is downward
Two equal charges q are connected by a spring of spring constant k and natural rest length L. The electrostatic repulsion stretches the spring so that the charges are a distance d apart. Part A What must be the magnitude of each of the charges q in terms of k, L, d and ϵ0? We are using k for the spring constant, so do not use the k from Coulomb's Law. Use the version with ϵ0 instead. AΣϕ |q| =
Four identical charges Q are placed at the corners of a square of side L. Part A Find the magnitude total force exerted on one charge by the other three charges. Express your answer in terms of the variables Q, L and appropriate constants. AΣϕ |F ⃗| =
A small 12.3 g plastic ball is tied to a very light 26.2 cm string that is attached to the vertical wall of a room. (See the figure (Figure 1).) A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of -1.40 µC, you observe that it remains suspended, with the string making an angle of 17.4 ◦ with the wall. Figure 1 of 1 Part A Find the magnitude of the electric field in the room. Express your answer in newtons per coulomb. AΣφ E = N/C ? Submit Request Answer Part B Find the direction of the electric field in the room. to the left to the right Submit Request Answer
Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a + r, a distance r to the right of the end of Q. (Figure 1) Figure 1 of 1 Part A Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a. Express your answer in terms some or all of the variables Q, a, x, and constant k. Part B Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a. Express your answer in terms some or all of the variables Q, a, y, r, and constant k. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms some or all of the variables Q, q, a, r, and constant k. Part D In what direction the charge distribution Q exerts force on q. to the left to the right
A uniformly charged ring has a radius 130.cm and a charge 19.5 µC. A small object with mass 6.00 g and charge -0.100 µC is at the center of the ring, but it is free to move along the axis of the ring. (It is not free to move off the axis. Part A Suppose the small object is displaced along the axis a distance z from the center of the ring. It is only displaced a very small amount, so z is much smaller than the radius of the ring. Show that the force is roughly proportional to the displacement, that is, that F ≈ αz, and find a numerical value for α. √ AΣφ α = N/m Part B We see from Part A that for small displacements the force behaves like a spring with spring constant α. If the object is displaced a very small distance away along the axis, find the frequency f in Hz with which it oscillates back and forth. √ AΣφ ? f = Hz