In Fig. 24-72, two particles of charges q1 and q2 are fixed to an x-axis. If a third particle, of charge , is brought from an infinite distance to point P, the three-particle system has the same electric potential energy as the original two-particle system. What is the charge ratio ?
The charge ratio is -1.66.
Draw the given figure as below.
Here, q1 and q2 are fixed charges.
Use the electric potential energy for the final three particle system,
If two like charges (two protons or two electrons) are brought towards each other, the potential energy of the system increases. If two unlike charges i.e. a proton and an electron are brought towards each other, the electric potential energy of the system decreases.
The electric potential is define by,
The bet potential is define by,
Where, U is electric potential energy, R is distance between the point charges, q is charge, is the permittivity of free space, and k is the Coulomb’s constant having a value
The net potential energy is,
According to the given condition,
Hence, the charge ratio is -1.66.
Two tiny metal spheres A and B, mass and , have equal positive charge . The spheres are connected by a mass less non-conducting string of length d=1.00 m, which is much greater than the radii of the spheres. (a) What is the electric potential energy of the system? (b) Suppose you cut the string. At that instant, what is the acceleration of each sphere? (c) A long time after you cut the string, what is the speed of each sphere?
Figure 24-47 shows a thin plastic rod of length L = 13.5cm and uniform charge 43.6 fC. (a) In terms of distance d, find an expression for the electric potential at point P1. (b) Next, substitute variable x for d and find an expression for the magnitude of the component Ex of the electric field at. (c) What is the direction of Ex relative to the positive direction of the x axis? (d) What is the value of Ex at P1 for x = d = 6.20cm? (e) From the symmetry in Fig. 24-47, determine Ey at P1.
The chocolate crumb mystery. This story begins with Problem 60 in Chapter 23. (a) From the answer to part (a) of that problem, find an expression for the electric potential as a function of the radial distance from the center of the pipe. (The electric potential is zero on the grounded pipe wall.) (b) For the typical volume charge density , what is the difference in the electric potential between the pipe’s center and its inside wall? (The story continues with Problem 60 in Chapter 25.)
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