Concept explainers
The speed of the proton.
Answer to Problem 36P
The speed of the proton is
Explanation of Solution
Write the expression for the total enclosed charge.
Here,
Write the expression for electric field force on the proton.
Here,
Substitute
Write the expression for centripetal force acting on the proton.
Here,
From Equation (III) and Equation (IV),
Rewrite the above equation for
Conclusion:
Substitute
Further solve the above equation.
Substitute
Therefore, the velocity of the proton is
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Chapter 24 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- A Two positively charged particles, each with charge Q, are held at positions (a, 0) and (a, 0) as shown in Figure P23.73. A third positively charged particle with charge q is placed at (0, h). a. Find an expression for the net electric force on the third particle with charge q. b. Show that the two charges Q behave like a single charge 2Q located at the origin when the distance h is much greater than a. Figure P23.73 Problems 73 and 74.arrow_forwardIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0 with the vertical. Determine the linear charge density of the rod. FIGURE P24.49arrow_forwardFigure P23.49 shows two identical small, charged spheres. One of mass 4.0 g is hanging by an insulating thread of length 20.0 cm. The other is held in place and has charge q1 = 3.6 C. The thread makes an angle of 18 with the vertical, resulting in the spheres being aligned horizontally, a distance r apart. Determine the charge q2 on the hanging sphere. Figure P23.49arrow_forward
- A metal sphere with charge +8.00 nC is attached to the left-hand end of a nonconducting rod of length L = 2.00 m. A second sphere with charge +2.00 nC is fixed to the right-hand end of the rod (Fig. P23.53). At what position d along the rod can a charged bead be placed for the bead to be in equilibrium? FIGURE P23.53arrow_forwardFind an expression for the magnitude of the electric field at point A mid-way between the two rings of radius R shown in Figure P24.30. The ring on the left has a uniform charge q1 and the ring on the right has a uniform charge q2. The rings are separated by distance d. Assume the positive x axis points to the right, through the center of the rings. FIGURE P24.30 Problems 30 and 31.arrow_forwardThree charged spheres are at rest in a plane as shown in Figure P23.70. Spheres A and B are fixed, but sphere C is attached to the ceiling by a lightweight thread. The tension in the string is 0.240 N. Spheres A and B have charges qA = 28.0 nC and qB = 28.0 nC. What charge is carried by sphere C?arrow_forward
- A Figure P23.65 shows two identical conducting spheres, each with charge q, suspended from light strings of length L. If the equilibrium angle the strings make with the vertical is , what is the mass m of the spheres? Figure P23.65arrow_forwardTwo small beads having positive charges q1 = 3q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in Figure P19.7, a third small, charged bead is free to slide on the rod. (a) At what position x is the third bead in equilibrium? (b) Can the equilibrium be stable?arrow_forwardA line of positive charge is formed into a semicircle of radius R = 60.0 cm as shown in Figure P23.41. The charge per unit length along the semicircle is given by the expression = 0 cos . The total charge on the semicircle is 12.0 C. Calculate the total total on a charge of 3.00 C placed at the center of curvature P. Figure P23.41arrow_forward
- Two small spherical conductors are suspended from light-weight vertical insulating threads. The conductors are brought into contact (Fig. P23.50, left) and released. Afterward, the conductors and threads stand apart as shown at right. a. What can you say about the charge of each sphere? b. Use the data given in Figure P23.50 to find the tension in each thread. c. Find the magnitude of the charge on each sphere. Figure P23.50arrow_forwardEight small conducting spheres with identical charge q = 2.00 C are placed at the corners of a cube of side d = 0.500 m (Fig. P23.75). What is the total force on the sphere at the origin (sphere A) due to the other seven spheres? Figure P23.75arrow_forwardFigure 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 P24.16arrow_forward
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