A particle of charge is released from rest at the point on an x-axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 40 cm if (a) and (b) ?
Using the concept of the conservation of energy and the formula of the electric potential energy, we can get the value of the final kinetic energy of the particle at the instant for different values of the charges.
The potential energy of the system due to point charges, (i)
Applying to the law of conservation of energy, (ii)
We have to apply conservation of energy to the particle with charge, which has zero initial kinetic energy. Thus, using this data in equation (ii), we get the equation of the final kinetic energy as follows:
The initial total energy of the particle is given using equation (i) as follows:
Since the particles repel each other the final separation distance between them is given as:
Potential energy at final position is given using equation (i) as follows:
Thus, the required kinetic energy at final position is given using equation (a) as follows:
Hence, the value of the kinetic energy is .
If the charge of the particle is
Now the particles attract each other so the final separation between them is:
Potential energy at the final position is given using equation (i) as follows:
Now, using the data in equation (a), the required kinetic energy at the instant is given as:
Hence, the value of the energy is 4.5 J.
In Fig. 24-31a, what is the potential at point P due to charge Q at distance R from P? Set at infinity. (b) In Fig. 24-31b, the same charge has been spread uniformly over a circular arc of radius R and central angle 40. What is the potential at point P, the center of curvature of the arc? (c) In Fig. 24-31c, the same charge Q has been spread uniformly over a circle of radius R . What is the potential at point P , the center of the circle? (d) Rank the three situations according to the magnitude of the electric field that is set up at P, greatest first.
Two large, parallel, conducting plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electric force of 3.9 x 10-15 N acts on an electron placed anywhere between the two plates. (Neglect fringing.) (a) Find the electric field at the position of the electron. (b) What is the potential difference between the plates?
Two metal spheres, each of radius 3.0 cm, have a center-to-center separation of 2.0 m. Sphere 1 has charge ; sphere 2 has charge . Assume that the separation is large enough for us to say that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With data-custom-editor="chemistry" at infinity, calculate (a) the potential at the point halfway between the centers and the potential on the surface of (b) sphere 1 and (c) sphere 2.
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